Acoustic wave device

ABSTRACT

An acoustic wave device includes a support substrate, a quartz-crystal layer provided directly or indirectly on the support substrate, a piezoelectric layer on the quartz-crystal layer, and an IDT electrode on the piezoelectric layer. When λ represents a wavelength defined by an electrode finger pitch of the IDT electrode, a thickness of the quartz-crystal layer is about 0.2λ or more and about 0.4λ or less, and the piezoelectric layer has a thickness smaller than the thickness of the quartz-crystal layer.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to Japanese PatentApplication No. 2020-175299 filed on Oct. 19, 2020 and is a ContinuationApplication of PCT Application No. PCT/JP2021/038418 filed on Oct. 18,2021. The entire contents of each application are hereby incorporatedherein by reference.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to an acoustic wave device.

2. Description of the Related Art

Acoustic wave devices have been widely used in, for example, filters ofcellular phones. International Publication No. 2018/164211 discloses anexample of a multiplexer in which an acoustic wave filter including anacoustic wave device is used. The acoustic wave device described inInternational Publication No. 2018/164211 includes an IDT (InterdigitalTransducer) electrode disposed on a multilayer substrate. The multilayersubstrate includes a silicon substrate, a silicon oxide layer, and apiezoelectric body that are stacked in this order. In the multiplexer,adjustment is performed so that a frequency of a higher-order mode ispositioned outside a pass band of the acoustic wave filter.

SUMMARY OF THE INVENTION

However, the acoustic wave device described in International PublicationNo. 2018/164211 has difficulty in sufficiently suppressing a rippleitself due to the higher-order mode.

Preferred embodiments of the present invention provide acoustic wavedevices each being capable of suppressing a higher-order mode in a wideband.

An acoustic wave device according to a preferred embodiment of thepresent disclosure includes a support substrate, a silicon oxide layerprovided directly or indirectly on the support substrate and havingcrystallinity, a piezoelectric layer on the silicon oxide layer havingcrystallinity, and an IDT electrode on the piezoelectric layer. When Arepresents a wavelength defined by an electrode finger pitch of the IDTelectrode, a thickness of the silicon oxide layer having crystallinityis about 0.2λ or more and about 0.4λ or less, and the piezoelectriclayer has a thickness smaller than the thickness of the silicon oxidelayer having crystallinity.

With the acoustic wave devices according to preferred embodiments of thepresent disclosure, a higher-order mode can be suppressed in a wideband.

The above and other elements, features, steps, characteristics andadvantages of the present invention will become more apparent from thefollowing detailed description of the preferred embodiments withreference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front sectional view of a portion of an acoustic wave deviceaccording to a first preferred embodiment of the present invention.

FIG. 2 is a plan view of the acoustic wave device according to the firstpreferred embodiment of the present invention.

FIG. 3 illustrates the phase characteristics of an acoustic wave devicehaving the configuration of the first preferred embodiment of thepresent invention and the phase characteristics of an acoustic wavedevice of a comparative example.

FIG. 4 illustrates the relationship between the thickness of aquartz-crystal layer and the phase of a higher-order mode.

FIG. 5 is an enlarged view of FIG. 4 .

FIG. 6 illustrates the relationship between φ_(q) in the azimuthalangles of the quartz-crystal layer, the cut angle of lithium tantalateof a piezoelectric layer, and the phase of a Rayleigh wave.

FIG. 7 illustrates the relationship between θ_(q) in the azimuthalangles of the quartz-crystal layer, the cut angle of the lithiumtantalate of the piezoelectric layer, and the phase of the Rayleighwave.

FIG. 8 illustrates the relationship between ψ_(q) in the azimuthalangles of the quartz-crystal layer, the cut angle of the lithiumtantalate of the piezoelectric layer, and the phase of the Rayleighwave.

FIG. 9 illustrates the relationship between φ_(q) in the azimuthalangles of the quartz-crystal layer, the cut angle of the lithiumtantalate of the piezoelectric layer, and the phase of a higher-ordermode.

FIG. 10 illustrates the relationship between θ_(q) in the azimuthalangles of the quartz-crystal layer, the cut angle of the lithiumtantalate of the piezoelectric layer, and the phase of the higher-ordermode.

FIG. 11 illustrates the relationship between ψ_(q) in the azimuthalangles of the quartz-crystal layer, the cut angle of the lithiumtantalate of the piezoelectric layer, and the phase of the higher-ordermode.

FIG. 12 illustrates the relationship between φ_(q) in the azimuthalangles of the quartz-crystal layer, the thickness of the quartz-crystallayer, and the phase of the Rayleigh wave.

FIG. 13 illustrates the relationship between θ_(q) in the azimuthalangles of the quartz-crystal layer, the thickness of the quartz-crystallayer, and the phase of the Rayleigh wave.

FIG. 14 illustrates the relationship between ψ_(q) in the azimuthalangles of the quartz-crystal layer, the thickness of the quartz-crystallayer, and the phase of the Rayleigh wave.

FIG. 15 illustrates the ranges of φ_(q) and θ_(q) in the azimuthalangles of the quartz-crystal layer, in which the Rayleigh wave can besuppressed.

FIG. 16 is a front sectional view of the vicinity of a pair of electrodefingers in a modification of the first preferred embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, the present invention will be clarified through thedescription of specific preferred embodiments thereof, with reference tothe drawings.

Note that preferred embodiments in the present description are examples,and the configurations in the different preferred embodiments can bepartially replaced from one to another or combined with one another.

FIG. 1 is a front sectional view of a portion of an acoustic wave deviceaccording to a first preferred embodiment of the present disclosure.FIG. 2 is a plan view of the acoustic wave device according to the firstpreferred embodiment. Note that FIG. 1 is a sectional view taken alongline I-I in FIG. 2 . In FIG. 2 , illustration of a protective film,which will be described later, is omitted.

As FIG. 1 illustrates, an acoustic wave device 1 includes a multilayersubstrate 6. The multilayer substrate 6 includes a support substrate 2,a quartz-crystal layer 4, and a piezoelectric layer 5. Morespecifically, the quartz-crystal layer 4 is disposed on the supportsubstrate 2. The piezoelectric layer 5 is disposed on the quartz-crystallayer 4.

In the present preferred embodiment, the support substrate 2 is asilicon substrate. However, the material for the support substrate 2 isnot limited to the above-described material. The quartz-crystal layer 4corresponds to a silicon oxide layer having crystallinity in the presentdisclosure. More specifically, the quartz-crystal layer 4 is amonocrystalline quartz-crystal layer in the present preferredembodiment. However, a layer corresponding to the quartz-crystal layer 4may be any silicon oxide layer having crystallinity. In the presentdescription, such a silicon oxide layer having crystallinity is regardedas equivalent to a silicon oxide layer having anisotropy in the materialconstants thereof. Examples of the silicon oxide layer havingcrystallinity include a silicon oxide layer having no piezoelectricity.Note that such a state of having anisotropy in the material constantsmeans that anisotropy is exhibited in at least one of the elasticconstant, the permittivity, the piezoelectric constant, the coefficientof linear expansion, and the thermal conductivity. The silicon oxidelayer having crystallinity may contain a crystal phase of, for example,tridymite, cristobalite, or coesite. When, inside the silicon oxidelayer having crystallinity, the percentage of orientation in a specificdirection is about 50% or more, the silicon oxide layer havingcrystallinity exhibits physical properties similar to those of quartzcrystal and exhibits Euler angle dependence as with quartz crystal.Thus, when the silicon oxide layer having crystallinity is used, effectssimilar to those exhibited when quartz crystal is used are also obtainedeven when the silicon oxide layer having crystallinity is not quartzcrystal. The crystallinity of the silicon oxide can be evaluated byusing the following methods. That is, for analyzing the crystalstructure, there can be used an X-ray diffraction method, electrondiffraction, electron backscattered diffraction (EBSD: ElectronBackScatter Diffraction), an Automated Crystal Orientation Mapping-TEMmethod (ACOM-TEM method), or a synchrotron radiation diffraction methodenabling analysis on a very minute structure.

In the present preferred embodiment, the piezoelectric layer 5 is alithium tantalate (LiTaO3) layer. However, the material for thepiezoelectric layer 5 is not limited to the above-described material.Examples of the material for the piezoelectric layer 5 include lithiumniobate.

Here, in the piezoelectric layer 5, (XLT, YLT, ZLT) represent thecrystallographic axes, and (φLT, θLT, ψLT) represent the azimuthalangles, and, in the quartz-crystal layer 4, (Xq, Yq, Zq) represent thecrystallographic axes, and (φq, θq, ψq) represent the azimuthal angles.In the present preferred embodiment, the piezoelectric layer 5 and thequartz-crystal layer 4 are stacked so that, when (φLT, θLT, ψLT) are(0°, 0°, 0°), and (φq, θq, ψq) are (0°, 0°, 0°), (XLT, YLT, ZLT)coincide with (Xq, Yq, Zq). Note that, in the present description, theazimuthal angles are given in Euler angle notation.

An IDT electrode 7 is disposed on the piezoelectric layer 5. Analternating voltage is applied to the IDT electrode 7, and an acousticwave is thereby excited. As FIG. 2 illustrates, a pair of reflectors 8Aand 8B is disposed on the piezoelectric layer 5 on both sides, in apropagation direction of an acoustic wave, of the IDT electrode 7. Asdescribed above, the acoustic wave device 1 of the present preferredembodiment is a surface acoustic wave resonator. Note that the acousticwave devices according to the present disclosure are not limited theretoand may be, for example, a filter device including plural surfaceacoustic wave resonators or a multiplexer.

As FIG. 2 illustrates, the IDT electrode 7 includes a first busbar 16, asecond busbar 17, plural first electrode fingers 18, and plural secondelectrode fingers 19. The first busbar 16 and the second busbar 17 faceone another. One end of each of the first electrode fingers 18 isconnected to the first busbar 16. One end of each of the secondelectrode fingers 19 is connected to the second busbar 17. The pluralfirst electrode fingers 18 and the plural second electrode fingers 19interdigitate with one another.

Each of the IDT electrode 7 and the reflectors 8A and 8B may include amultilayer metal film or a single-layer metal film.

Here, when λ represents a wavelength defined by the electrode fingerpitch of the IDT electrode 7, the thickness of the quartz-crystal layer4 is about 0.2λ or more and about 0.4λ or less, for example. Moreover,the piezoelectric layer 5 has a thickness smaller than the thickness ofthe quartz-crystal layer 4. Note that the electrode finger pitch refersto a distance between the centers of adjacent ones of the electrodefingers. Specifically, the electrode finger pitch refers to a distancebetween the center points, in the propagation direction of the acousticwave, of adjacent ones of the electrode fingers.

Referring back to FIG. 1 , a protective film 9 is disposed on thepiezoelectric layer 5 so as to cover the IDT electrode 7. The IDTelectrode 7 is hardly broken with the protective film 9. As for theprotective film 9, an appropriate dielectric can be used. For example,when silicon oxide is used for the protective film 9, a temperaturecoefficient of frequency (TCF) can be increased. When silicon nitride isused for the protective film 9, a frequency can be easily adjustedthrough adjustment of the thickness of the protective film 9. However,the protective film 9 is not necessarily disposed.

Some of the unique features of the present preferred embodiment include,in the multilayer substrate 6, the support substrate 2, thequartz-crystal layer 4, and the piezoelectric layer 5 are stacked, thequartz-crystal layer 4 has a thickness of about 0.2λ or more and about0.4λ or less, and the piezoelectric layer 5 has a thickness smaller thanthe thickness of the quartz-crystal layer 4. However, as describedabove, a layer corresponding to the quartz-crystal layer 4 may be thesilicon oxide layer having crystallinity. With the configuration, ahigher-order mode can be suppressed in a wide band. Such suppression ofa higher-order mode in a wide band will be demonstrated below throughcomparison between the present preferred embodiment and a comparativeexample. Note that the comparative example differs from the presentpreferred embodiment in that a multilayer substrate has noquartz-crystal layer. More specifically, the multilayer substrate of thecomparative example is a multilayer body including a support substrate,a silicon nitride film, a silicon oxide film, and a piezoelectric layer.

The phase characteristics of an acoustic wave device having theconfiguration of the present preferred embodiment and the phasecharacteristics of an acoustic wave device of the comparative examplewere measured. The design parameters of the acoustic wave device havingthe configuration of the present preferred embodiment are as follows.

Support substrate 2; material . . . Si

Quartz-crystal layer 4; material . . . monocrystalline SiO2, thickness .. . 600 nm, azimuthal angles (φq, θq, ψq) . . . (45°, 90°, 90°)

Piezoelectric layer 5; material . . . LiTaO3, thickness . . . 400 nm,cut angle . . . 40° Y

IDT electrode 7; material . . . Ti/AlCu/Ti, thickness 12 nm/100 nm/4 nm

Wavelength λ of IDT electrode 7; 2 μm

FIG. 3 illustrates the phase characteristics of the acoustic wave devicehaving the configuration of the first preferred embodiment and the phasecharacteristics of the acoustic wave device of the comparative example.

From FIG. 3 , it is clear that, in the comparative example, a largespurious emission due to a higher-order mode occurs in the vicinity ofthe frequency indicated by arrow A. Specifically, at the frequencyindicated by arrow A, the phase of the higher-order mode in thecomparative example is 40 deg. In contrast, in the first preferredembodiment, the higher-order mode in the vicinity of the frequencyindicated by arrow A is suppressed. Moreover, it is clear that, in thefirst preferred embodiment, the higher-order mode is suppressed to lessthan about −80 deg. in a wide band.

In addition, in the comparative example, a large spurious emission dueto a Rayleigh wave occurs at the frequency indicated by arrow B. Incontrast, it is clear that, in the first preferred embodiment, such aRayleigh wave can also be suppressed.

Moreover, it will be demonstrated below that the higher-order mode canbe suppressed by the quartz-crystal layer having a thickness of about0.2λ or more and about 0.4λ or less. In the acoustic wave device havinga multilayer substrate whose layer configuration is similar to that ofthe first preferred embodiment, the phase of the higher-order mode wasmeasured while the thickness of the quartz-crystal layer was changed.The thickness of the quartz-crystal layer was changed in a range ofabout 200 nm or more and about 1300 nm or less in increments of about100 nm, for example. Note that, because the wavelength λ is defined asabout 2 μm, the thickness of the quartz-crystal layer varies in a rangeof about 0.1λ or more and about 0.65λ or less in increments of about0.05λ, for example.

FIG. 4 illustrates the relationship between the thickness of thequartz-crystal layer and the phase of the higher-order mode. FIG. 5 isan enlarged view of FIG. 4 .

From FIG. 4 and FIG. 5 , it is clear that, when the thickness of thequartz-crystal layer is less than about 0.2λ and is more than about0.4λ, the values of the phase of the higher-order mode are larger thanabout −70 deg, for example. In contrast, it is clear that, when thethickness of the quartz-crystal layer is about 0.2λ or more and about0.4λ or less as in the first preferred embodiment, the higher-order modeis suppressed to less than about −70 deg, for example. Thus, in thefirst preferred embodiment, the higher-order mode can be effectivelysuppressed. In addition, when the thickness of the quartz-crystal layeris about 0.2λ or more and about 0.4λ or less, for example, thepiezoelectric layer has a thickness smaller than the thickness of thequartz-crystal layer.

As described above, in the first preferred embodiment, in addition tothe higher-order mode, the Rayleigh wave can also be suppressed. Thestudy conducted by the inventors of the present application has revealedthat, when the cut angle of the piezoelectric body of the piezoelectriclayer 5 is changed, the azimuthal angles of the quartz-crystal layer 4at which the Rayleigh wave can be suppressed are also changed. At thispoint, there was obtained the relationship between the cut angle of thepiezoelectric body of the piezoelectric layer 5 and the azimuthal anglesof the quartz-crystal layer 4; and the phase of the Rayleigh wave. Notethat, regarding the azimuthal angles of the quartz-crystal layer 4, φq,θq, and ψq in (φq, 10°, 0°), (0°, θq, 0°), and (0°, 10°, ψq) werechanged. The cut angle of lithium tantalate of the piezoelectric layer 5was about 30° Y, about 50° Y, or about 70° Y.

FIG. 6 illustrates the relationship between φq in the azimuthal anglesof the quartz-crystal layer, the cut angle of the lithium tantalate ofthe piezoelectric layer, and the phase of the Rayleigh wave.

As FIG. 6 illustrates, when the cut angle is about 30° Y, the Rayleighwave is effectively suppressed in the ranges of about 10°≤φq≤about 45°,about 80°≤φq≤about 105°, and about 130° ≤φq≤about 165°. Note that, here,such a state of effectively suppressing the Rayleigh wave refers to astate where values of the phase of the Rayleigh wave are within therange from the minimum value of the phase of the Rayleigh wave to avalue about 40 deg. larger than the minimum value. Except wherespecifically noted, the same applies to the following description. Whenthe cut angle is about 50° Y, the Rayleigh wave is effectivelysuppressed in the ranges of about 0°≤φq≤about 25° and about 95°≤φq≤about145°. When the cut angle is 70° Y, the Rayleigh wave is effectivelysuppressed in the ranges of about 0°≤φq≤about 15° and about100°≤φq≤about 135°, for example.

FIG. 7 illustrates the relationship between θq in the azimuthal anglesof the quartz-crystal layer, the cut angle of the lithium tantalate ofthe piezoelectric layer, and the phase of the Rayleigh wave.

As FIG. 7 illustrates, when the cut angle is about 30° Y, the Rayleighwave is effectively suppressed in the ranges of about 15°≤θq≤about 35°and about 75°≤θq≤about 115°. When the cut angle is about 50° Y, theRayleigh wave is effectively suppressed in the ranges of about0°≤θq≤about 25° and about 110°≤θq≤about 180°, for example. When the cutangle is about 70° Y, the Rayleigh wave is effectively suppressed in theranges of about 0°≤θq≤about 15° and about 160°≤θq≤about 180°, forexample.

FIG. 8 illustrates the relationship between ψq in the azimuthal anglesof the quartz-crystal layer, the cut angle of the lithium tantalate ofthe piezoelectric layer, and the phase of the Rayleigh wave.

As FIG. 8 illustrates, when the cut angle is about 30° Y, the Rayleighwave is effectively suppressed in the ranges of about 10°≤ψq≤about 40°,about 70° ψq about 100°, and about 145° ≤ψq≤about 180°, for example.When the cut angle is about 50° Y, the Rayleigh wave is effectivelysuppressed in the ranges of about 0°≤ψq≤about 25° and about 90°≤ψq≤about150°, for example. When the cut angle is about 70° Y, the Rayleigh waveis effectively suppressed in the ranges of about 0°≤ψq≤about 20° andabout 100°≤ψq≤about 140°, for example.

In the above-described comparative example, as FIG. 3 illustrates, thephase of the higher-order mode is 40 deg. In contrast, with theconfiguration of the multilayer substrate 6 in the first preferredembodiment, the higher-order mode can be suppressed even when φq, θq,and ψq in the azimuthal angles of the quartz-crystal layer 4 arechanged. Such suppression of the higher-order mode will be demonstratedbelow. Note that the measurement of the phase of the higher-order modewas conducted under conditions similar to the conditions under which therelationships in FIGS. 6 to 8 were obtained.

FIG. 9 illustrates the relationship between φq in the azimuthal anglesof the quartz-crystal layer, the cut angle of the lithium tantalate ofthe piezoelectric layer, and the phase of the higher-order mode. FIG. 10illustrates the relationship between θ_(q) in the azimuthal angles ofthe quartz-crystal layer, the cut angle of the lithium tantalate of thepiezoelectric layer, and the phase of the higher-order mode. FIG. 11illustrates the relationship between ψq in the azimuthal angles of thequartz-crystal layer, the cut angle of the lithium tantalate of thepiezoelectric layer, and the phase of the higher-order mode.

From FIG. 9 , it is clear that, regardless of φq in the azimuthal anglesof the quartz-crystal layer 4, the higher-order mode can be suppressedto less than about 40 deg., more specifically, less than about −30 deg,for example. Similarly, from FIG. 10 and FIG. 11 , it is clear that,regardless of θq and ψq, the higher-order mode can be further suppressedthan in the above-described comparative example.

As described above, the higher-order mode can be suppressed in the firstpreferred embodiment. Moreover, the Rayleigh wave can also beeffectively suppressed through adjustment of the azimuthal angles of thequartz-crystal layer 4.

At this point, it was confirmed that the phase of the Rayleigh wave haslow dependency on the thickness of the quartz-crystal layer 4. Morespecifically, the phase of the Rayleigh wave was measured in each of thecases of about 0.2λ, about 0.3λ, and about 0.4λ in thicknesses of thequartz-crystal layer 4, while an azimuthal angle was changed. Note that,regarding the azimuthal angles of the quartz-crystal layer 4, φq, θq,and ψq in (φq, 120°, 90°, (70°, θq, 90°), and (70°, 120°, ψq) werechanged.

FIG. 12 illustrates the relationship between φq in the azimuthal anglesof the quartz-crystal layer, the thickness of the quartz-crystal layer,and the phase of the Rayleigh wave. FIG. 13 illustrates the relationshipbetween θq in the azimuthal angles of the quartz-crystal layer, thethickness of the quartz-crystal layer, and the phase of the Rayleighwave. FIG. 14 illustrates the relationship between ψ₄ in the azimuthalangles of the quartz-crystal layer, the thickness of the quartz-crystallayer, and the phase of the Rayleigh wave.

From FIG. 12 , it is clear that, when the thickness of thequartz-crystal layer 4 is about 0.2λ or more and about 0.4λ or less, therelationship between: φq in the azimuthal angles of the quartz-crystallayer 4; and the phase of the Rayleigh wave does not vary greatly.Similarly, from FIG. 13 and FIG. 14 , it is clear that, when thethickness of the quartz-crystal layer 4 is about 0.2λ or more and about0.4λ or less, the relationships between: ϵq and ψq in the azimuthalangles of the quartz-crystal layer 4; and the phase of the Rayleigh wavedo not vary greatly.

Examples of the relationship between an azimuthal angle of thequartz-crystal layer 4, the cut angle of the lithium tantalate of thepiezoelectric layer 5, and the phase of the Rayleigh wave are givenabove. The relationship will be further detailed below.

FIG. 15 illustrates the ranges of φq and θq in the azimuthal angles ofthe quartz-crystal layer, in which the Rayleigh wave can be suppressed.Note that the ranges in FIG. 15 are each a range when ψq in theazimuthal angles of the quartz-crystal layer 4 is about 0°, and the cutangle of the lithium tantalate of the piezoelectric layer 5 is about 30°Y.

When the cut angle of the lithium tantalate of the piezoelectric layer 5is about 30° Y, the Rayleigh wave can be effectively suppressed in theranges of (φq, θq, 0°) represented by the hatched areas in FIG. 15 . Therelationship is given in Table 1. Here, it has been clear that, when thecut angle is about 20° Y or more and less than about 40° Y, for example,the Rayleigh wave can also be suppressed in ranges of the azimuthalangles, similar to the ranges of the azimuthal angles in the case ofabout 30° Y in cut angle. Thus, in Table 1, the case where the cut angleis about 20° Y or more and less than about 40° Y is given, for example.Moreover, the Rayleigh wave can also be suppressed in a similar mannerwithin the range of about ±5° or ±10° of each of φq, θq, and ψq, forexample. Thus, the range of about ±5° or ±10° of each of φq, θq, and ψqis given in the tables in the present description, for example.

Similarly, the ranges of φq and θq in which the Rayleigh wave can besuppressed were obtained while the cut angle of the lithium tantalate ofthe piezoelectric layer 5 and ψq in the azimuthal angles of thequartz-crystal layer 4 were changed. The results therefrom are given inTables 2 to 10.

The Rayleigh wave can be suppressed when the cut angle of the lithiumtantalate of the piezoelectric layer 5 is about 20° Y or more and lessthan about 40° Y and if φq, θq, and ψq in the azimuthal angles of thequartz-crystal layer 4 are in any one of the combinations in Tables 1 to10. Note that the quartz-crystal layer 4 is a monocrystallinequartz-crystal layer.

TABLE 1 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  15 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 2 −5 ≤ φ_(q) < 5   75 ≤θ_(q) ≤ 135 −10 ≤ ψ_(q) < 10 3  5 ≤ φ_(q) < 15  5 ≤ θ_(q) ≤ 35 −10 ≤ψ_(q) < 10 4  5 ≤ φ_(q) < 15  65 ≤ θ_(q) ≤ 115 −10 ≤ ψ_(q) < 10 5 15 ≤φ_(q) < 25  5 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 6 15 ≤ φ_(q) < 25  65 ≤θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 7 15 ≤ φ_(q) < 25 175 ≤ θ_(q) ≤ 185 −10 ≤ψ_(q) < 10 8 25 ≤ φ_(q) < 35  −5 ≤ θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 9 25 ≤φ_(q) < 35 155 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 10 35 ≤ φ_(q) < 45  −5 ≤θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 11 35 ≤ φ_(q) < 45 155 ≤ θ_(q) ≤ 185 −10 ≤ψ_(q) < 10 12 45 ≤ φ_(q) < 55 25 ≤ θ_(q) ≤ 95 −10 ≤ ψ_(q) < 10 13 45 ≤φ_(q) < 55 145 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 14 55 ≤ φ_(q) < 65 25 ≤θ_(q) ≤ 95 −10 ≤ ψ_(q) < 10 15 55 ≤ φ_(q) < 65 145 ≤ θ_(q) ≤ 175 −10 ≤ψ_(q) < 10 16 65 ≤ φ_(q) < 75 25 ≤ θ_(q) ≤ 95 −10 ≤ ψ_(q) < 10 17 65 ≤φ_(q) < 75 145 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 18 75 ≤ φ_(q) < 85 −5 ≤θ_(q) ≤ 95 −10 ≤ ψ_(q) < 10 19 75 ≤ φ_(q) < 85 155 ≤ θ_(q) ≤ 185 −10 ≤ψ_(q) < 10 20 85 ≤ φ_(q) < 95 −5 ≤ θ_(q) ≤ 45 −10 ≤ ψ_(q) < 10 21 85 ≤φ_(q) < 95  55 ≤ θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 22 85 ≤ φ_(q) < 95 155 ≤θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 23  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 35 −10 ≤ψ_(q) < 10 24  95 ≤ φ_(q) < 105  65 ≤ θ_(q) ≤ 115 −10 ≤ ψ_(q) < 10 25105 ≤ φ_(q) < 115 15 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 26 105 ≤ φ_(q) < 115 75 ≤ θ_(q) ≤ 125 −10 ≤ ψ_(q) < 10 27 115 ≤ φ_(q) < 125 15 ≤ θ_(q) ≤ 35−10 ≤ ψ_(q) < 10 28 115 ≤ φ_(q) < 125  75 ≤ θ_(q) ≤ 135 −10 ≤ ψ_(q) < 1029 125 ≤ φ_(q) < 135  5 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 30 125 ≤ φ_(q) <135  65 ≤ θ_(q) ≤ 115 −10 ≤ ψ_(q) < 10 31 135 ≤ φ_(q) < 145  5 ≤ θ_(q) ≤35 −10 ≤ ψ_(q) < 10 32 135 ≤ φ_(q) < 145  65 ≤ θ_(q) ≤ 105 −10 ≤ ψ_(q) <10 33 135 ≤ φ_(q) < 145 175 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 34 145 ≤φ_(q) < 155  −5 ≤ θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 35 145 ≤ φ_(q) < 155 155≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 36 155 ≤ φ_(q) < 165  −5 ≤ θ_(q) ≤ 105−10 ≤ ψ_(q) < 10 37 155 ≤ φ_(q) < 165 155 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 1038 165 ≤ φ_(q) < 175 25 ≤ θ_(q) ≤ 95 −10 ≤ ψ_(q) < 10 39 165 ≤ φ_(q) <175 145 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 40  175 ≤ φ_(q) ≤ 185 25 ≤ θ_(q)≤ 95 −10 ≤ ψ_(q) < 10 41  175 ≤ φ_(q) ≤ 185 145 ≤ θ_(q) ≤ 175 −10 ≤ψ_(q) < 10

TABLE 2 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   5 ≤ θ_(q) ≤ 35 10 ≤ ψ_(q) < 30 2 −5 ≤ φ_(q) < 5   65 ≤ θ_(q)≤ 145 10 ≤ ψ_(q) < 30 3  5 ≤ φ_(q) < 15  −5 ≤ θ_(q) ≤ 145 10 ≤ ψ_(q) <30 4 15 ≤ φ_(q) < 25  −5 ≤ θ_(q) ≤ 135 10 ≤ ψ_(q) < 30 5 25 ≤ φ_(q) < 35 25 ≤ θ_(q) ≤ 135 10 ≤ ψ_(q) < 30 6 35 ≤ φ_(q) < 45  25 ≤ θ_(q) ≤ 125 10≤ ψ_(q) < 30 7 35 ≤ φ_(q) < 45 175 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 8 45 ≤φ_(q) < 55  25 ≤ θ_(q) ≤ 105 10 ≤ ψ_(q) < 30 9 45 ≤ φ_(q) < 55 165 ≤θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 10 55 ≤ φ_(q) < 65  −5 ≤ θ_(q) ≤ 105 10 ≤ψ_(q) < 30 11 55 ≤ φ_(q) < 65 155 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 12 65 ≤φ_(q) < 75  −5 ≤ θ_(q) ≤ 105 10 ≤ ψ_(q) < 30 13 65 ≤ φ_(q) < 75 145 ≤θ_(q) ≤ 175 10 ≤ ψ_(q) < 30 14 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 45 10 ≤ψ_(q) < 30 15 75 ≤ φ_(q) < 85 75 ≤ θ_(q) ≤ 95 10 ≤ ψ_(q) < 30 16 75 ≤φ_(q) < 85 145 ≤ θ_(q) ≤ 165 10 ≤ ψ_(q) < 30 17 85 ≤ φ_(q) < 95 15 ≤θ_(q) ≤ 35 10 ≤ ψ_(q) < 30 18 85 ≤ φ_(q) < 95 75 ≤ θ_(q) ≤ 95 10 ≤ ψ_(q)< 30 19 85 ≤ φ_(q) < 95 145 ≤ θ_(q) ≤ 175 10 ≤ ψ_(q) < 30 20  95 ≤ φ_(q)< 105 15 ≤ θ_(q) ≤ 35 10 ≤ ψ_(q) < 30 21  95 ≤ φ_(q) < 105 65 ≤ θ_(q) ≤95 10 ≤ ψ_(q) < 30 22  95 ≤ φ_(q) < 105 145 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) <30 23 105 ≤ φ_(q) < 115 15 ≤ θ_(q) ≤ 35 10 ≤ ψ_(q) < 30 24 105 ≤ φ_(q) <115 65 ≤ θ_(q) ≤ 95 10 ≤ ψ_(q) < 30 25 105 ≤ φ_(q) < 115 145 ≤ θ_(q) ≤185 10 ≤ ψ_(q) < 30 26 115 ≤ φ_(q) < 125  5 ≤ θ_(q) ≤ 35 10 ≤ ψ_(q) < 3027 115 ≤ φ_(q) < 125  65 ≤ θ_(q) ≤ 145 10 ≤ ψ_(q) < 30 28 125 ≤ φ_(q) <135  −5 ≤ θ_(q) ≤ 145 10 ≤ ψ_(q) < 30 29 135 ≤ φ_(q) < 145  −5 ≤ θ_(q) ≤135 10 ≤ ψ_(q) < 30 30 145 ≤ φ_(q) < 155  25 ≤ θ_(q) ≤ 135 10 ≤ ψ_(q) <30 31 155 ≤ φ_(q) < 165  25 ≤ θ_(q) ≤ 115 10 ≤ ψ_(q) < 30 32 155 ≤ φ_(q)< 165 175 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 33 165 ≤ φ_(q) < 175  25 ≤ θ_(q)≤ 105 10 ≤ ψ_(q) < 30 34 165 ≤ φ_(q) < 175 165 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q)< 30 35  175 ≤ φ_(q) ≤ 185  −5 ≤ θ_(q) ≤ 105 10 ≤ ψ_(q) < 30 36  175 ≤φ_(q) ≤ 185 155 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30

TABLE 3 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 85 30 ≤ ψ_(q) < 50 2 −5 ≤ φ_(q) < 5  125 ≤ θ_(q)≤ 185 30 ≤ ψ_(q) < 50 3  5 ≤ φ_(q) < 15 25 ≤ θ_(q) ≤ 75 30 ≤ ψ_(q) < 504  5 ≤ φ_(q) < 15 125 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 5 15 ≤ φ_(q) < 25 25≤ θ_(q) ≤ 55 30 ≤ ψ_(q) < 50 6 15 ≤ φ_(q) < 25 65 ≤ θ_(q) ≤ 85 30 ≤ψ_(q) < 50 7 15 ≤ φ_(q) < 25 125 ≤ θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 8 25 ≤φ_(q) < 35 15 ≤ θ_(q) ≤ 55 30 ≤ ψ_(q) < 50 9 25 ≤ φ_(q) < 35 115 ≤ θ_(q)≤ 145 30 ≤ ψ_(q) < 50 10 35 ≤ φ_(q) < 45 −5 ≤ θ_(q) ≤ 45 30 ≤ ψ_(q) < 5011 35 ≤ φ_(q) < 45  75 ≤ θ_(q) ≤ 145 30 ≤ ψ_(q) < 50 12 45 ≤ φ_(q) < 55−5 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 13 45 ≤ φ_(q) < 55  75 ≤ θ_(q) ≤ 135 30≤ ψ_(q) < 50 14 55 ≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 15 55 ≤φ_(q) < 65  85 ≤ θ_(q) ≤ 135 30 ≤ ψ_(q) < 50 16 55 ≤ φ_(q) < 65 175 ≤θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 17 65 ≤ φ_(q) < 75 15 ≤ θ_(q) ≤ 45 30 ≤ψ_(q) < 50 18 65 ≤ φ_(q) < 75  75 ≤ θ_(q) ≤ 115 30 ≤ ψ_(q) < 50 19 65 ≤φ_(q) < 75 155 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 20 75 ≤ φ_(q) < 85 15 ≤θ_(q) ≤ 45 30 ≤ ψ_(q) < 50 21 75 ≤ φ_(q) < 85  75 ≤ θ_(q) ≤ 105 30 ≤ψ_(q) < 50 22 75 ≤ φ_(q) < 85 145 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 23 85 ≤φ_(q) < 95 15 ≤ θ_(q) ≤ 45 30 ≤ ψ_(q) < 50 24 85 ≤ φ_(q) < 95 55 ≤ θ_(q)≤ 95 30 ≤ ψ_(q) < 50 25 85 ≤ φ_(q) < 95 145 ≤ θ_(q) ≤ 165 30 ≤ ψ_(q) <50 26  95 ≤ φ_(q) < 105  5 ≤ θ_(q) ≤ 95 30 ≤ ψ_(q) < 50 27  95 ≤ φ_(q) <105 145 ≤ θ_(q) ≤ 165 30 ≤ ψ_(q) < 50 28 105 ≤ φ_(q) < 115 −5 ≤ θ_(q) ≤85 30 ≤ ψ_(q) < 50 29 105 ≤ φ_(q) < 115 135 ≤ θ_(q) ≤ 175 30 ≤ ψ_(q) <50 30 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 85 30 ≤ ψ_(q) < 50 31 115 ≤ φ_(q) <125 125 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 32 125 ≤ φ_(q) < 135 25 ≤ θ_(q) ≤75 30 ≤ ψ_(q) < 50 33 125 ≤ φ_(q) < 135 125 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) <50 34 135 ≤ φ_(q) < 145 25 ≤ θ_(q) ≤ 55 30 ≤ ψ_(q) < 50 35 135 ≤ φ_(q) <145 65 ≤ θ_(q) ≤ 85 30 ≤ ψ_(q) < 50 36 135 ≤ φ_(q) < 145 125 ≤ θ_(q) ≤155 30 ≤ ψ_(q) < 50 37 145 ≤ φ_(q) < 155 15 ≤ θ_(q) ≤ 55 30 ≤ ψ_(q) < 5038 145 ≤ φ_(q) < 155 65 ≤ θ_(q) ≤ 75 30 ≤ ψ_(q) < 50 39 145 ≤ φ_(q) <155 115 ≤ θ_(q) ≤ 145 30 ≤ ψ_(q) < 50 40 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤45 30 ≤ ψ_(q) < 50 41 155 ≤ φ_(q) < 165  75 ≤ θ_(q) ≤ 145 30 ≤ ψ_(q) <50 42 165 ≤ φ_(q) < 175 −5 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 43 165 ≤ φ_(q) <175  75 ≤ θ_(q) ≤ 135 30 ≤ ψ_(q) < 50 44  175 ≤ φ_(q) ≤ 185 −5 ≤ θ_(q) ≤65 30 ≤ ψ_(q) < 50 45  175 ≤ φ_(q) ≤ 185  85 ≤ θ_(q) ≤ 135 30 ≤ ψ_(q) <50 46  175 ≤ φ_(q) ≤ 185 175 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50

TABLE 4 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  25 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 2 −5 ≤ φ_(q) < 5  125 ≤ θ_(q)≤ 165 50 ≤ ψ_(q) < 70 3  5 ≤ φ_(q) < 15 15 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 704  5 ≤ φ_(q) < 15 105 ≤ θ_(q) ≤ 165 50 ≤ ψ_(q) < 70 5 15 ≤ φ_(q) < 25 −5≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 6 15 ≤ φ_(q) < 25  75 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 7 25 ≤ φ_(q) < 35  −5 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 8 35 ≤φ_(q) < 45  −5 ≤ θ_(q) ≤ 175 50 ≤ ψ_(q) < 70 9 45 ≤ φ_(q) < 55 25 ≤θ_(q) ≤ 85 50 ≤ ψ_(q) < 70 10 45 ≤ φ_(q) < 55  95 ≤ θ_(q) ≤ 145 50 ≤ψ_(q) < 70 11 55 ≤ φ_(q) < 65 25 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 12 55 ≤φ_(q) < 65  75 ≤ θ_(q) ≤ 145 50 ≤ ψ_(q) < 70 13 65 ≤ φ_(q) < 75  15 ≤θ_(q) ≤ 135 50 ≤ ψ_(q) < 70 14 75 ≤ φ_(q) < 85  5 ≤ θ_(q) ≤ 125 50 ≤ψ_(q) < 70 15 75 ≤ φ_(q) < 85 175 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 16 85 ≤φ_(q) < 95  −5 ≤ θ_(q) ≤ 105 50 ≤ ψ_(q) < 70 17 85 ≤ φ_(q) < 95 145 ≤θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 18  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 85 50 ≤ψ_(q) < 70 19  95 ≤ φ_(q) < 105 135 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 20 105≤ φ_(q) < 115 25 ≤ θ_(q) ≤ 75 50 ≤ ψ_(q) < 70 21 105 ≤ φ_(q) < 115 125 ≤θ_(q) ≤ 165 50 ≤ ψ_(q) < 70 22 115 ≤ φ_(q) < 125 25 ≤ θ_(q) ≤ 65 50 ≤ψ_(q) < 70 23 115 ≤ φ_(q) < 125 125 ≤ θ_(q) ≤ 165 50 ≤ ψ_(q) < 70 24 125≤ φ_(q) < 135 15 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 25 125 ≤ φ_(q) < 135 105 ≤θ_(q) ≤ 165 50 ≤ ψ_(q) < 70 26 135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 65 50 ≤ψ_(q) < 70 27 135 ≤ φ_(q) < 145  75 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 28 145≤ φ_(q) < 155  −5 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 29 155 ≤ φ_(q) < 165  −5≤ θ_(q) ≤ 175 50 ≤ ψ_(q) < 70 30 165 ≤ φ_(q) < 175 25 ≤ θ_(q) ≤ 85 50 ≤ψ_(q) < 70 31 165 ≤ φ_(q) < 175  95 ≤ θ_(q) ≤ 145 50 ≤ ψ_(q) < 70 32 175 ≤ φ_(q) ≤ 185  25 ≤ θ_(q) ≤ 145 50 ≤ ψ_(q) < 70

TABLE 5 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 95  70 ≤ ψ_(q) < 90 2 −5 ≤ φ_(q) < 5  105 ≤θ_(q) ≤ 185  70 ≤ ψ_(q) < 90 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 165 70 ≤ψ_(q) < 90 4 15 ≤ φ_(q) < 25 −5 ≤ θ_(q) ≤ 155 70 ≤ ψ_(q) < 90 5 25 ≤φ_(q) < 35 35 ≤ θ_(q) ≤ 165 70 ≤ ψ_(q) < 90 6 35 ≤ φ_(q) < 45 35 ≤ θ_(q)≤ 185 70 ≤ ψ_(q) < 90 7 45 ≤ φ_(q) < 55 25 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 908 55 ≤ φ_(q) < 65  5 ≤ θ_(q) ≤ 175 70 ≤ ψ_(q) < 90 9 65 ≤ φ_(q) < 75 −5≤ θ_(q) ≤ 145 70 ≤ ψ_(q) < 90 10 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 135 70 ≤ψ_(q) < 90 11 85 ≤ φ_(q) < 95 25 ≤ θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 12  95 ≤φ_(q) < 105 25 ≤ θ_(q) ≤ 155 70 ≤ ψ_(q) < 90 13  95 ≤ φ_(q) < 105 175 ≤θ_(q) ≤ 185  70 ≤ ψ_(q) < 90 14 105 ≤ φ_(q) < 115 15 ≤ θ_(q) ≤ 95  70 ≤ψ_(q) < 90 15 105 ≤ φ_(q) < 115 105 ≤ θ_(q) ≤ 185  70 ≤ ψ_(q) < 90 16115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 95  70 ≤ ψ_(q) < 90 17 115 ≤ φ_(q) < 125105 ≤ θ_(q) ≤ 185  70 ≤ ψ_(q) < 90 18 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 16570 ≤ ψ_(q) < 90 19 135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 155 70 ≤ ψ_(q) < 90 20145 ≤ φ_(q) < 155 35 ≤ θ_(q) ≤ 165 70 ≤ ψ_(q) < 90 21 155 ≤ φ_(q) < 16535 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 22 165 ≤ φ_(q) < 175 25 ≤ θ_(q) ≤ 18570 ≤ ψ_(q) < 90 23  175 ≤ φ_(q) ≤ 185  5 ≤ θ_(q) ≤ 175 70 ≤ ψ_(q) < 90

TABLE 6 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 5  90 ≤ ψ_(q) < 110 2 −5 ≤ φ_(q) < 5  15 ≤ θ_(q)≤ 185 90 ≤ ψ_(q) < 110 3  5 ≤ φ_(q) < 15 25 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) <110 4 15 ≤ φ_(q) < 25 35 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 5 25 ≤ φ_(q) <35 45 ≤ θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 6 35 ≤ φ_(q) < 45 5 ≤ θ_(q) ≤ 15 90≤ ψ_(q) < 110 7 35 ≤ φ_(q) < 45 25 ≤ θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 8 45 ≤φ_(q) < 55 −5 ≤ θ_(q) ≤ 165 90 ≤ ψ_(q) < 110 9 55 ≤ φ_(q) < 65 −5 ≤θ_(q) ≤ 75  90 ≤ ψ_(q) < 110 10 55 ≤ φ_(q) < 65 95 ≤ θ_(q) ≤ 185 90 ≤ψ_(q) < 110 11 65 ≤ φ_(q) < 75 15 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 12 75 ≤φ_(q) < 85 25 ≤ θ_(q) ≤ 175 90 ≤ ψ_(q) < 110 13 85 ≤ φ_(q) < 95 15 ≤θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 14  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 145 90 ≤ψ_(q) < 110 15 105 ≤ φ_(q) < 115 −5 ≤ θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 16115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 5  90 ≤ ψ_(q) < 110 17 115 ≤ φ_(q) < 12515 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 18 125 ≤ φ_(q) < 135 25 ≤ θ_(q) ≤ 18590 ≤ ψ_(q) < 110 19 135 ≤ φ_(q) < 145 35 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 11020 145 ≤ φ_(q) < 155 45 ≤ θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 21 155 ≤ φ_(q) <165 5 ≤ θ_(q) ≤ 15 90 ≤ ψ_(q) < 110 22 155 ≤ φ_(q) < 165 25 ≤ θ_(q) ≤155 90 ≤ ψ_(q) < 110 23 165 ≤ φ_(q) < 175 −5 ≤ θ_(q) ≤ 165 90 ≤ ψ_(q) <110 24  175 ≤ φ_(q) ≤ 185 −5 ≤ θ_(q) ≤ 75  90 ≤ ψ_(q) < 110 25  175 ≤φ_(q) ≤ 185 95 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110

TABLE 7 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  35 ≤ θ_(q) ≤ 95 110 ≤ ψ_(q) < 130 2 −5 ≤ φ_(q) < 5  105 ≤θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 3  5 ≤ φ_(q) < 15  45 ≤ θ_(q) ≤ 165 110 ≤ψ_(q) < 130 4 15 ≤ φ_(q) < 25  45 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 5 25 ≤φ_(q) < 35 −5 ≤ θ_(q) ≤ 35 110 ≤ ψ_(q) < 130 6 25 ≤ φ_(q) < 35  65 ≤θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 7 35 ≤ φ_(q) < 45 −5 ≤ θ_(q) ≤ 45 110 ≤ψ_(q) < 130 8 35 ≤ φ_(q) < 45  85 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 9 45 ≤φ_(q) < 55 15 ≤ θ_(q) ≤ 45 110 ≤ ψ_(q) < 130 10 45 ≤ φ_(q) < 55 105 ≤θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 11 55 ≤ φ_(q) < 65 15 ≤ θ_(q) ≤ 55 110 ≤ψ_(q) < 130 12 55 ≤ φ_(q) < 65 115 ≤ θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 13 65≤ φ_(q) < 75  5 ≤ θ_(q) ≤ 65 110 ≤ ψ_(q) < 130 14 65 ≤ φ_(q) < 75 125 ≤θ_(q) ≤ 165 110 ≤ ψ_(q) < 130 15 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 75 110 ≤ψ_(q) < 130 16 75 ≤ φ_(q) < 85 125 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 17 85≤ φ_(q) < 95  −5 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 18  95 ≤ φ_(q) < 105 −5≤ θ_(q) ≤ 5  110 ≤ ψ_(q) < 130 19  95 ≤ φ_(q) < 105 15 ≤ θ_(q) ≤ 85 110≤ ψ_(q) < 130 20  95 ≤ φ_(q) < 105  95 ≤ θ_(q) ≤ 175 110 ≤ ψ_(q) < 13021 105 ≤ φ_(q) < 115  25 ≤ θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 22 115 ≤ φ_(q)< 125 35 ≤ θ_(q) ≤ 95 110 ≤ ψ_(q) < 130 23 115 ≤ φ_(q) < 125 105 ≤ θ_(q)≤ 155 110 ≤ ψ_(q) < 130 24 125 ≤ φ_(q) < 135  45 ≤ θ_(q) ≤ 165 110 ≤ψ_(q) < 130 25 135 ≤ φ_(q) < 145  45 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 26145 ≤ φ_(q) < 155 −5 ≤ θ_(q) ≤ 35 110 ≤ ψ_(q) < 130 27 145 ≤ φ_(q) < 155 65 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 28 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤ 45110 ≤ ψ_(q) < 130 29 155 ≤ φ_(q) < 165  85 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) <130 30 165 ≤ φ_(q) < 175 15 ≤ θ_(q) ≤ 45 110 ≤ ψ_(q) < 130 31 165 ≤φ_(q) < 175 105 ≤ θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 32  175 ≤ φ_(q) ≤ 185 15≤ θ_(q) ≤ 55 110 ≤ ψ_(q) < 130 33  175 ≤ φ_(q) ≤ 185 115 ≤ θ_(q) ≤ 155110 ≤ ψ_(q) < 130

TABLE 8 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   45 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 2 −5 ≤ φ_(q) < 5  115 ≤θ_(q) ≤ 175 130 ≤ ψ_(q) < 150 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 25 130 ≤ψ_(q) < 150 4  5 ≤ φ_(q) < 15  65 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 5  5 ≤φ_(q) < 15 125 ≤ θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 6 15 ≤ φ_(q) < 25 −5 ≤θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 7 15 ≤ φ_(q) < 25  65 ≤ θ_(q) ≤ 105 130 ≤ψ_(q) < 150 8 15 ≤ φ_(q) < 25 135 ≤ θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 9 25 ≤φ_(q) < 35  5 ≤ θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 10 25 ≤ φ_(q) < 35  75 ≤θ_(q) ≤ 115 130 ≤ ψ_(q) < 150 11 25 ≤ φ_(q) < 35 135 ≤ θ_(q) ≤ 165 130 ≤ψ_(q) < 150 12 35 ≤ φ_(q) < 45 15 ≤ θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 13 35 ≤φ_(q) < 45  85 ≤ θ_(q) ≤ 125 130 ≤ ψ_(q) < 150 14 35 ≤ φ_(q) < 45 145 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 15 45 ≤ φ_(q) < 55  5 ≤ θ_(q) ≤ 45 130 ≤ψ_(q) < 150 16 45 ≤ φ_(q) < 55  95 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 17 55≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 45 130 ≤ ψ_(q) < 150 18 55 ≤ φ_(q) < 65  95 ≤θ_(q) ≤ 145 130 ≤ ψ_(q) < 150 19 55 ≤ φ_(q) < 65 165 ≤ θ_(q) ≤ 185 130 ≤ψ_(q) < 150 20 65 ≤ φ_(q) < 75 −5 ≤ θ_(q) ≤ 55 130 ≤ ψ_(q) < 150 21 65 ≤φ_(q) < 75 105 ≤ θ_(q) ≤ 155 130 ≤ ψ_(q) < 150 22 75 ≤ φ_(q) < 85 −5 ≤θ_(q) ≤ 5  130 ≤ ψ_(q) < 150 23 75 ≤ φ_(q) < 85 15 ≤ θ_(q) ≤ 55 130 ≤ψ_(q) < 150 24 75 ≤ φ_(q) < 85 65 ≤ θ_(q) ≤ 85 130 ≤ ψ_(q) < 150 25 75 ≤φ_(q) < 85  95 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 26 75 ≤ φ_(q) < 85 115 ≤θ_(q) ≤ 155 130 ≤ ψ_(q) < 150 27 85 ≤ φ_(q) < 95 35 ≤ θ_(q) ≤ 65 130 ≤ψ_(q) < 150 28 85 ≤ φ_(q) < 95 85 ≤ θ_(q) ≤ 95 130 ≤ ψ_(q) < 150 29 85 ≤φ_(q) < 95 115 ≤ θ_(q) ≤ 125 130 ≤ ψ_(q) < 150 30 85 ≤ φ_(q) < 95 135 ≤θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 31  95 ≤ φ_(q) < 105 35 ≤ θ_(q) ≤ 95 130 ≤ψ_(q) < 150 32  95 ≤ φ_(q) < 105 115 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 33105 ≤ φ_(q) < 115 45 ≤ θ_(q) ≤ 95 130 ≤ ψ_(q) < 150 34 105 ≤ φ_(q) < 115135 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 35 115 ≤ φ_(q) < 125  45 ≤ θ_(q) ≤105 130 ≤ ψ_(q) < 150 36 115 ≤ φ_(q) < 125 115 ≤ θ_(q) ≤ 175 130 ≤ ψ_(q)< 150 37 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 25 130 ≤ ψ_(q) < 150 38 125 ≤φ_(q) < 135  65 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 39 125 ≤ φ_(q) < 135 125≤ θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 40 135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 35 130≤ ψ_(q) < 150 41 135 ≤ φ_(q) < 145  65 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 15042 135 ≤ φ_(q) < 145 135 ≤ θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 43 145 ≤ φ_(q)< 155  5 ≤ θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 44 145 ≤ φ_(q) < 155  75 ≤ θ_(q)≤ 115 130 ≤ ψ_(q) < 150 45 145 ≤ φ_(q) < 155 135 ≤ θ_(q) ≤ 165 130 ≤ψ_(q) < 150 46 155 ≤ φ_(q) < 165 15 ≤ θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 47155 ≤ φ_(q) < 165  85 ≤ θ_(q) ≤ 125 130 ≤ ψ_(q) < 150 48 155 ≤ φ_(q) <165 145 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 49 165 ≤ φ_(q) < 175  5 ≤ θ_(q)≤ 45 130 ≤ ψ_(q) < 150 50 165 ≤ φ_(q) < 175  95 ≤ θ_(q) ≤ 185 130 ≤ψ_(q) < 150 51  175 ≤ φ_(q) ≤ 185 −5 ≤ θ_(q) ≤ 45 130 ≤ ψ_(q) < 150 52 175 ≤ φ_(q) ≤ 185  95 ≤ θ_(q) ≤ 145 130 ≤ ψ_(q) < 150 53  175 ≤ φ_(q) ≤185 165 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150

TABLE 9 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 35  150 ≤ ψ_(q) < 170 2 −5 ≤ φ_(q) < 5  75 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 3  5 ≤ φ_(q) < 15 5 ≤ θ_(q) ≤ 35 150 ≤ψ_(q) < 170 4  5 ≤ φ_(q) < 15 75 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 5 15 ≤φ_(q) < 25 5 ≤ θ_(q) ≤ 35 150 ≤ ψ_(q) < 170 6 15 ≤ φ_(q) < 25 75 ≤ θ_(q)≤ 105 150 ≤ ψ_(q) < 170 7 15 ≤ φ_(q) < 25 135 ≤ θ_(q) ≤ 175  150 ≤ ψ_(q)< 170 8 25 ≤ φ_(q) < 35 5 ≤ θ_(q) ≤ 35 150 ≤ ψ_(q) < 170 9 25 ≤ φ_(q) <35 75 ≤ θ_(q) ≤ 105 150 ≤ ψ_(q) < 170 10 25 ≤ φ_(q) < 35 145 ≤ θ_(q) ≤165  150 ≤ ψ_(q) < 170 11 35 ≤ φ_(q) < 45 −5 ≤ θ_(q) ≤ 35  150 ≤ ψ_(q) <170 12 35 ≤ φ_(q) < 45 85 ≤ θ_(q) ≤ 115 150 ≤ ψ_(q) < 170 13 35 ≤ φ_(q)< 45 145 ≤ θ_(q) ≤ 165  150 ≤ ψ_(q) < 170 14 45 ≤ φ_(q) < 55 −5 ≤ θ_(q)≤ 35  150 ≤ ψ_(q) < 170 15 45 ≤ φ_(q) < 55 85 ≤ θ_(q) ≤ 115 150 ≤ ψ_(q)< 170 16 45 ≤ φ_(q) < 55 145 ≤ θ_(q) ≤ 165  150 ≤ ψ_(q) < 170 17 55 ≤φ_(q) < 65 −5 ≤ θ_(q) ≤ 5  150 ≤ ψ_(q) < 170 18 55 ≤ φ_(q) < 65 65 ≤θ_(q) ≤ 115 150 ≤ ψ_(q) < 170 19 55 ≤ φ_(q) < 65 145 ≤ θ_(q) ≤ 185  150≤ ψ_(q) < 170 20 65 ≤ φ_(q) < 75 45 ≤ θ_(q) ≤ 125 150 ≤ ψ_(q) < 170 2165 ≤ φ_(q) < 75 155 ≤ θ_(q) ≤ 185  150 ≤ ψ_(q) < 170 22 75 ≤ φ_(q) < 8545 ≤ θ_(q) ≤ 145 150 ≤ ψ_(q) < 170 23 75 ≤ φ_(q) < 85 155 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 24 85 ≤ φ_(q) < 95 45 ≤ θ_(q) ≤ 155 150 ≤ ψ_(q) < 17025  95 ≤ φ_(q) < 105 65 ≤ θ_(q) ≤ 155 150 ≤ ψ_(q) < 170 26 105 ≤ φ_(q) <115 −5 ≤ θ_(q) ≤ 15  150 ≤ ψ_(q) < 170 27 105 ≤ φ_(q) < 115 75 ≤ θ_(q) ≤165 150 ≤ ψ_(q) < 170 28 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 35  150 ≤ ψ_(q)< 170 29 115 ≤ φ_(q) < 125 75 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 30 125 ≤φ_(q) < 135 5 ≤ θ_(q) ≤ 35 150 ≤ ψ_(q) < 170 31 125 ≤ φ_(q) < 135 75 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 32 135 ≤ φ_(q) < 145 5 ≤ θ_(q) ≤ 35 150 ≤ψ_(q) < 170 33 135 ≤ φ_(q) < 145 75 ≤ θ_(q) ≤ 105 150 ≤ ψ_(q) < 170 34135 ≤ φ_(q) < 145 135 ≤ θ_(q) ≤ 175  150 ≤ ψ_(q) < 170 35 145 ≤ φ_(q) <155 5 ≤ θ_(q) ≤ 35 150 ≤ ψ_(q) < 170 36 145 ≤ φ_(q) < 155 75 ≤ θ_(q) ≤105 150 ≤ ψ_(q) < 170 37 145 ≤ φ_(q) < 155 145 ≤ θ_(q) ≤ 165  150 ≤ψ_(q) < 170 38 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤ 35  150 ≤ ψ_(q) < 170 39155 ≤ φ_(q) < 165 85 ≤ θ_(q) ≤ 115 150 ≤ ψ_(q) < 170 40 155 ≤ φ_(q) <165 145 ≤ θ_(q) ≤ 165  150 ≤ ψ_(q) < 170 41 165 ≤ φ_(q) < 175 −5 ≤ θ_(q)≤ 35  150 ≤ ψ_(q) < 170 42 165 ≤ φ_(q) < 175 85 ≤ θ_(q) ≤ 115 150 ≤ψ_(q) < 170 43 165 ≤ φ_(q) < 175 145 ≤ θ_(q) ≤ 165  150 ≤ ψ_(q) < 170 44 175 ≤ φ_(q) ≤ 185 −5 ≤ θ_(q) ≤ 5  150 ≤ ψ_(q) < 170 45  175 ≤ φ_(q) ≤185 55 ≤ θ_(q) ≤ 115 150 ≤ ψ_(q) < 170 46  175 ≤ φ_(q) ≤ 185 145 ≤ θ_(q)≤ 185  150 ≤ ψ_(q) < 170

TABLE 10 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  5 ≤ θ_(q) ≤ 35 170 ≤ ψ_(q) ≤ 190 2 −5 ≤ φ_(q) < 5  85 ≤ θ_(q)≤ 155 170 ≤ ψ_(q) ≤ 190 3  5 ≤ φ_(q) < 15 5 ≤ θ_(q) ≤ 35 170 ≤ ψ_(q) ≤190 4  5 ≤ φ_(q) < 15 85 ≤ θ_(q) ≤ 155 170 ≤ ψ_(q) ≤ 190 5 15 ≤ φ_(q) <25 −5 ≤ θ_(q) ≤ 25  170 ≤ ψ_(q) ≤ 190 6 15 ≤ φ_(q) < 25 75 ≤ θ_(q) ≤ 185170 ≤ ψ_(q) ≤ 190 7 25 ≤ φ_(q) < 35 −5 ≤ θ_(q) ≤ 25  170 ≤ ψ_(q) ≤ 190 825 ≤ φ_(q) < 35 75 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 9 35 ≤ φ_(q) < 45 −5≤ θ_(q) ≤ 5  170 ≤ ψ_(q) ≤ 190 10 35 ≤ φ_(q) < 45 75 ≤ θ_(q) ≤ 115 170 ≤ψ_(q) ≤ 190 11 35 ≤ φ_(q) < 45 145 ≤ θ_(q) ≤ 175  170 ≤ ψ_(q) ≤ 190 1245 ≤ φ_(q) < 55 65 ≤ θ_(q) ≤ 115 170 ≤ ψ_(q) ≤ 190 13 45 ≤ φ_(q) < 55145 ≤ θ_(q) ≤ 175  170 ≤ ψ_(q) ≤ 190 14 55 ≤ φ_(q) < 65 45 ≤ θ_(q) ≤ 105170 ≤ ψ_(q) ≤ 190 15 55 ≤ φ_(q) < 65 145 ≤ θ_(q) ≤ 165  170 ≤ ψ_(q) ≤190 16 65 ≤ φ_(q) < 75 55 ≤ θ_(q) ≤ 105 170 ≤ ψ_(q) ≤ 190 17 65 ≤ φ_(q)< 75 145 ≤ θ_(q) ≤ 165  170 ≤ ψ_(q) ≤ 190 18 75 ≤ φ_(q) < 85 65 ≤ θ_(q)≤ 115 170 ≤ ψ_(q) ≤ 190 19 75 ≤ φ_(q) < 85 145 ≤ θ_(q) ≤ 185  170 ≤ψ_(q) ≤ 190 20 85 ≤ φ_(q) < 95 −5 ≤ θ_(q) ≤ 25  170 ≤ ψ_(q) ≤ 190 21 85≤ φ_(q) < 95 75 ≤ θ_(q) ≤ 125 170 ≤ ψ_(q) ≤ 190 22 85 ≤ φ_(q) < 95 135 ≤θ_(q) ≤ 185  170 ≤ ψ_(q) ≤ 190 23  105 ≤ φ_(q) ≤ 115 5 ≤ θ_(q) ≤ 35 170≤ ψ_(q) ≤ 190

On the other hand, it has been clear that the Rayleigh wave can besuppressed when the cut angle of the lithium tantalate of thepiezoelectric layer 5 is about 40° Y or more and about 90° Y or less, insimilar ranges of the azimuthal angles of the quartz-crystal layer 4,for example. Thus, in Tables 11 to 20, there are given the ranges of theazimuthal angles in which the Rayleigh wave can be suppressed when thecut angle is about 40° Y or more and about 90° Y or less, for example.

The Rayleigh wave can be suppressed when the cut angle of the lithiumtantalate of the piezoelectric layer 5 is about 40° Y or more and about90° Y or less and if φ_(q), θ_(q), and ψ_(q) in the azimuthal angles ofthe quartz-crystal layer 4 are in any one of the combinations in Tables11 to 20, for example. Note that the quartz-crystal layer 4 is amonocrystalline quartz-crystal layer.

TABLE 11 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 25  −10 ≤ ψ_(q) < 10 2 −5 ≤ φ_(q) < 5  105 ≤θ_(q) ≤ 185  −10 ≤ ψ_(q) < 10 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 25  −10 ≤ψ_(q) < 10 4  5 ≤ φ_(q) < 15 105 ≤ θ_(q) ≤ 185  −10 ≤ ψ_(q) < 10 5 15 ≤φ_(q) < 25 −5 ≤ θ_(q) ≤ 15  −10 ≤ ψ_(q) < 10 6 15 ≤ φ_(q) < 25 95 ≤θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 7 25 ≤ φ_(q) < 35 95 ≤ θ_(q) ≤ 175 −10 ≤ψ_(q) < 10 8 35 ≤ φ_(q) < 45 95 ≤ θ_(q) ≤ 165 −10 ≤ ψ_(q) < 10 9 45 ≤φ_(q) < 55 95 ≤ θ_(q) ≤ 155 −10 ≤ ψ_(q) < 10 10 55 ≤ φ_(q) < 65 95 ≤θ_(q) ≤ 155 −10 ≤ ψ_(q) < 10 11 65 ≤ φ_(q) < 75 95 ≤ θ_(q) ≤ 155 −10 ≤ψ_(q) < 10 12 75 ≤ φ_(q) < 85 95 ≤ θ_(q) ≤ 165 −10 ≤ ψ_(q) < 10 13 85 ≤φ_(q) < 95 95 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 14  95 ≤ φ_(q) < 105 −5 ≤θ_(q) ≤ 15  −10 ≤ ψ_(q) < 10 15  95 ≤ φ_(q) < 105 95 ≤ θ_(q) ≤ 185 −10 ≤ψ_(q) < 10 16 105 ≤ φ_(q) < 115 −5 ≤ θ_(q) ≤ 25  −10 ≤ ψ_(q) < 10 17 105≤ φ_(q) < 115 95 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 18 115 ≤ φ_(q) < 125 −5≤ θ_(q) ≤ 25  −10 ≤ ψ_(q) < 10 19 115 ≤ φ_(q) < 125 105 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 20 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 25  −10 ≤ ψ_(q) < 1021 125 ≤ φ_(q) < 135 105 ≤ θ_(q) ≤ 185  −10 ≤ ψ_(q) < 10 22 135 ≤ φ_(q)< 145 −5 ≤ θ_(q) ≤ 15  −10 ≤ ψ_(q) < 10 23 135 ≤ φ_(q) < 145 95 ≤ θ_(q)≤ 185 −10 ≤ ψ_(q) < 10 24 145 ≤ φ_(q) < 155 95 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q)< 10 25 155 ≤ φ_(q) < 165 95 ≤ θ_(q) ≤ 165 −10 ≤ ψ_(q) < 10 26 165 ≤φ_(q) < 175 95 ≤ θ_(q) ≤ 155 −10 ≤ ψ_(q) < 10 27 175 ≤ φ_(q) < 185 95 ≤θ_(q) ≤ 155 −10 ≤ ψ_(q) < 10

TABLE 12 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 15  10 ≤ ψ_(q) < 30 2 −5 ≤ φ_(q) < 5  95 ≤ θ_(q)≤ 185 10 ≤ ψ_(q) < 30 3  5 ≤ φ_(q) < 15 115 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) <30 4 15 ≤ φ_(q) < 25 105 ≤ θ_(q) ≤ 115  10 ≤ ψ_(q) < 30 5 15 ≤ φ_(q) <25 125 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 30 6 25 ≤ φ_(q) < 35 115 ≤ θ_(q) ≤185  10 ≤ ψ_(q) < 30 7 35 ≤ φ_(q) < 45 105 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) <30 8 45 ≤ φ_(q) < 55 95 ≤ θ_(q) ≤ 175 10 ≤ ψ_(q) < 30 9 55 ≤ φ_(q) < 6595 ≤ θ_(q) ≤ 165 10 ≤ ψ_(q) < 30 10 65 ≤ φ_(q) < 75 95 ≤ θ_(q) ≤ 155 10≤ ψ_(q) < 30 11 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 25  10 ≤ ψ_(q) < 30 12 75 ≤φ_(q) < 85 95 ≤ θ_(q) ≤ 155 10 ≤ ψ_(q) < 30 13 85 ≤ φ_(q) < 95 −5 ≤θ_(q) ≤ 25  10 ≤ ψ_(q) < 30 14 85 ≤ φ_(q) < 95 95 ≤ θ_(q) ≤ 155 10 ≤ψ_(q) < 30 15  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 25  10 ≤ ψ_(q) < 30 16  95≤ φ_(q) < 105 95 ≤ θ_(q) ≤ 155 10 ≤ ψ_(q) < 30 17 105 ≤ φ_(q) < 115 −5 ≤θ_(q) ≤ 25  10 ≤ ψ_(q) < 30 18 105 ≤ φ_(q) < 115 95 ≤ θ_(q) ≤ 175 10 ≤ψ_(q) < 30 19 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 15  10 ≤ ψ_(q) < 30 20 115≤ φ_(q) < 125 95 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 21 125 ≤ φ_(q) < 135 115≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 30 22 135 ≤ φ_(q) < 145 105 ≤ θ_(q) ≤ 115 10 ≤ ψ_(q) < 30 23 135 ≤ φ_(q) < 145 125 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 3024 145 ≤ φ_(q) < 155 115 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 30 25 155 ≤ φ_(q) <165 105 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 30 26 165 ≤ φ_(q) < 175 95 ≤ θ_(q) ≤175 10 ≤ ψ_(q) < 30 27 175 ≤ φ_(q) < 185 95 ≤ θ_(q) ≤ 165 10 ≤ ψ_(q) <30

TABLE 13 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   75 ≤ θ_(q) ≤ 105 30 ≤ ψ_(q) < 50 2 −5 ≤ φ_(q) < 5  115 ≤θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 3  5 ≤ φ_(q) < 15 65 ≤ θ_(q) ≤ 95 30 ≤ ψ_(q)< 50 4  5 ≤ φ_(q) < 15 115 ≤ θ_(q) ≤ 175 30 ≤ ψ_(q) < 50 5 15 ≤ φ_(q) <25 65 ≤ θ_(q) ≤ 75 30 ≤ ψ_(q) < 50 6 15 ≤ φ_(q) < 25 145 ≤ θ_(q) ≤ 18530 ≤ ψ_(q) < 50 7 25 ≤ φ_(q) < 35 55 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 8 25 ≤φ_(q) < 35 135 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 9 35 ≤ φ_(q) < 45 135 ≤θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 10 45 ≤ φ_(q) < 55 125 ≤ θ_(q) ≤ 185 30 ≤ψ_(q) < 50 11 55 ≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 25 30 ≤ ψ_(q) < 50 12 55 ≤φ_(q) < 65 115 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 13 65 ≤ φ_(q) < 75 −5 ≤θ_(q) ≤ 35 30 ≤ ψ_(q) < 50 14 65 ≤ φ_(q) < 75 115 ≤ θ_(q) ≤ 175 30 ≤ψ_(q) < 50 15 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 25 30 ≤ ψ_(q) < 50 16 75 ≤φ_(q) < 85  95 ≤ θ_(q) ≤ 165 30 ≤ ψ_(q) < 50 17 85 ≤ φ_(q) < 95 −5 ≤θ_(q) ≤ 25 30 ≤ ψ_(q) < 50 18 85 ≤ φ_(q) < 95  95 ≤ θ_(q) ≤ 155 30 ≤ψ_(q) < 50 19  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 15 30 ≤ ψ_(q) < 50 20  95 ≤φ_(q) < 105  85 ≤ θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 21 105 ≤ φ_(q) < 115  85 ≤θ_(q) ≤ 145 30 ≤ ψ_(q) < 50 22 115 ≤ φ_(q) < 125  75 ≤ θ_(q) ≤ 105 30 ≤ψ_(q) < 50 23 115 ≤ φ_(q) < 125 115 ≤ θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 24 125≤ φ_(q) < 135 65 ≤ θ_(q) ≤ 95 30 ≤ ψ_(q) < 50 25 125 ≤ φ_(q) < 135 115 ≤θ_(q) ≤ 175 30 ≤ ψ_(q) < 50 26 135 ≤ φ_(q) < 145 65 ≤ θ_(q) ≤ 75 30 ≤ψ_(q) < 50 27 135 ≤ φ_(q) < 145 145 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 28 145≤ φ_(q) < 155 55 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 29 145 ≤ φ_(q) < 155 135 ≤θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 30 155 ≤ φ_(q) < 165 135 ≤ θ_(q) ≤ 185 30 ≤ψ_(q) < 50 31 165 ≤ φ_(q) < 175 125 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 32 175≤ φ_(q) < 185 −5 ≤ θ_(q) ≤ 25 30 ≤ ψ_(q) < 50 33 175 ≤ φ_(q) < 185 115 ≤θ_(q) ≤ 185 30 ≤ ψ_(q) < 50

TABLE 14 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   55 ≤ θ_(q) ≤ 135 50 ≤ ψ_(q) < 70 2  5 ≤ φ_(q) < 15  55 ≤θ_(q) ≤ 135 50 ≤ ψ_(q) < 70 3 15 ≤ φ_(q) < 25  45 ≤ θ_(q) ≤ 115 50 ≤ψ_(q) < 70 4 25 ≤ φ_(q) < 35 45 ≤ θ_(q) ≤ 85 50 ≤ ψ_(q) < 70 5 25 ≤φ_(q) < 35 165 ≤ θ_(q) ≤ 175 50 ≤ ψ_(q) < 70 6 35 ≤ φ_(q) < 45 −5 ≤θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 7 35 ≤ φ_(q) < 45 145 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 8 45 ≤ φ_(q) < 55 −5 ≤ θ_(q) ≤ 45 50 ≤ ψ_(q) < 70 9 45 ≤φ_(q) < 55 135 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 10 55 ≤ φ_(q) < 65 −5 ≤θ_(q) ≤ 35 50 ≤ ψ_(q) < 70 11 55 ≤ φ_(q) < 65 125 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 12 65 ≤ φ_(q) < 75 −5 ≤ θ_(q) ≤ 35 50 ≤ ψ_(q) < 70 13 65 ≤φ_(q) < 75 125 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 14 75 ≤ φ_(q) < 85 −5 ≤θ_(q) ≤ 25 50 ≤ ψ_(q) < 70 15 75 ≤ φ_(q) < 85 115 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 16 85 ≤ φ_(q) < 95  95 ≤ θ_(q) ≤ 175 50 ≤ ψ_(q) < 70 17  95 ≤φ_(q) < 105  75 ≤ θ_(q) ≤ 155 50 ≤ ψ_(q) < 70 18 105 ≤ φ_(q) < 115  65 ≤θ_(q) ≤ 145 50 ≤ ψ_(q) < 70 19 115 ≤ φ_(q) < 125  65 ≤ θ_(q) ≤ 135 50 ≤ψ_(q) < 70 20 125 ≤ φ_(q) < 135  55 ≤ θ_(q) ≤ 135 50 ≤ ψ_(q) < 70 21 135≤ φ_(q) < 145  45 ≤ θ_(q) ≤ 115 50 ≤ ψ_(q) < 70 22 145 ≤ φ_(q) < 155 45≤ θ_(q) ≤ 85 50 ≤ ψ_(q) < 70 23 145 ≤ φ_(q) < 155 165 ≤ θ_(q) ≤ 175 50 ≤ψ_(q) < 70 24 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 25 155 ≤φ_(q) < 165 145 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 26 165 ≤ φ_(q) < 175 −5 ≤θ_(q) ≤ 45 50 ≤ ψ_(q) < 70 27 165 ≤ φ_(q) < 175 135 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 28 175 ≤ φ_(q) < 185 −5 ≤ θ_(q) ≤ 35 50 ≤ ψ_(q) < 70 29 175 ≤φ_(q) < 185 125 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70

TABLE 15 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   55 ≤ θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 2  5 ≤ φ_(q) < 15 25 ≤θ_(q) ≤ 35 70 ≤ ψ_(q) < 90 3  5 ≤ φ_(q) < 15  45 ≤ θ_(q) ≤ 135 70 ≤ψ_(q) < 90 4 15 ≤ φ_(q) < 25  −5 ≤ θ_(q) ≤ 115 70 ≤ ψ_(q) < 90 5 25 ≤φ_(q) < 35 −5 ≤ θ_(q) ≤ 65 70 ≤ ψ_(q) < 90 6 35 ≤ φ_(q) < 45 −5 ≤ θ_(q)≤ 55 70 ≤ ψ_(q) < 90 7 45 ≤ φ_(q) < 55 −5 ≤ θ_(q) ≤ 45 70 ≤ ψ_(q) < 90 855 ≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 35 70 ≤ ψ_(q) < 90 9 55 ≤ φ_(q) < 65 135 ≤θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 10 65 ≤ φ_(q) < 75 125 ≤ θ_(q) ≤ 185 70 ≤ψ_(q) < 90 11 75 ≤ φ_(q) < 85 115 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 12 85 ≤φ_(q) < 95  85 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 13  95 ≤ φ_(q) < 105  65 ≤θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 14 105 ≤ φ_(q) < 115  55 ≤ θ_(q) ≤ 175 70 ≤ψ_(q) < 90 15 115 ≤ φ_(q) < 125  55 ≤ θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 16 125≤ φ_(q) < 135 25 ≤ θ_(q) ≤ 35 70 ≤ ψ_(q) < 90 17 125 ≤ φ_(q) < 135  45 ≤θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 18 135 ≤ φ_(q) < 145  −5 ≤ θ_(q) ≤ 115 70 ≤ψ_(q) < 90 19 135 ≤ φ_(q) < 145 125 ≤ θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 20 145≤ φ_(q) < 155 −5 ≤ θ_(q) ≤ 65 70 ≤ ψ_(q) < 90 21 155 ≤ φ_(q) < 165 −5 ≤θ_(q) ≤ 55 70 ≤ ψ_(q) < 90 22 165 ≤ φ_(q) < 175 −5 ≤ θ_(q) ≤ 45 70 ≤ψ_(q) < 90 23 175 ≤ φ_(q) < 185 −5 ≤ θ_(q) ≤ 35 70 ≤ ψ_(q) < 90 24 175 ≤φ_(q) < 185 135 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 90

TABLE 16 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 45 90 ≤ ψ_(q) < 110 2 −5 ≤ φ_(q) < 5  135 ≤θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 45 90 ≤ψ_(q) < 110 4  5 ≤ φ_(q) < 15 165 ≤ θ_(q) ≤ 175 90 ≤ ψ_(q) < 110 5 15 ≤φ_(q) < 25 −5 ≤ θ_(q) ≤ 65 90 ≤ ψ_(q) < 110 6 25 ≤ φ_(q) < 35 −5 ≤ θ_(q)≤ 65 90 ≤ ψ_(q) < 110 7 35 ≤ φ_(q) < 45 −5 ≤ θ_(q) ≤ 75 90 ≤ ψ_(q) < 1108 45 ≤ φ_(q) < 55  15 ≤ θ_(q) ≤ 115 90 ≤ ψ_(q) < 110 9 45 ≤ φ_(q) < 55175 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 10 55 ≤ φ_(q) < 65  35 ≤ θ_(q) ≤ 12590 ≤ ψ_(q) < 110 11 65 ≤ φ_(q) < 75  55 ≤ θ_(q) ≤ 145 90 ≤ ψ_(q) < 11012 75 ≤ φ_(q) < 85  55 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 13 85 ≤ φ_(q) < 95 65 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 14  95 ≤ φ_(q) < 105  85 ≤ θ_(q) ≤105 90 ≤ ψ_(q) < 110 15  95 ≤ φ_(q) < 105 115 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) <110 16 105 ≤ φ_(q) < 115 125 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 17 115 ≤φ_(q) < 125 −5 ≤ θ_(q) ≤ 45 90 ≤ ψ_(q) < 110 18 115 ≤ φ_(q) < 125 135 ≤θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 19 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 45 90 ≤ψ_(q) < 110 20 125 ≤ φ_(q) < 135 165 ≤ θ_(q) ≤ 175 90 ≤ ψ_(q) < 110 21135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 65 90 ≤ ψ_(q) < 110 22 145 ≤ φ_(q) < 155−5 ≤ θ_(q) ≤ 65 90 ≤ ψ_(q) < 110 23 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤ 75 90≤ ψ_(q) < 110 24 165 ≤ φ_(q) < 175  15 ≤ θ_(q) ≤ 115 90 ≤ ψ_(q) < 110 25175 ≤ φ_(q) < 185  35 ≤ θ_(q) ≤ 125 90 ≤ ψ_(q) < 110

TABLE 17 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 45 110 ≤ ψ_(q) < 130 2 −5 ≤ φ_(q) < 5  145 ≤θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 55 110 ≤ψ_(q) < 130 4  5 ≤ φ_(q) < 15 145 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 5 15 ≤φ_(q) < 25 −5 ≤ θ_(q) ≤ 55 110 ≤ ψ_(q) < 130 6 15 ≤ φ_(q) < 25 155 ≤θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 7 25 ≤ φ_(q) < 35  5 ≤ θ_(q) ≤ 75 110 ≤ψ_(q) < 130 8 35 ≤ φ_(q) < 45 25 ≤ θ_(q) ≤ 95 110 ≤ ψ_(q) < 130 9 45 ≤φ_(q) < 55  35 ≤ θ_(q) ≤ 105 110 ≤ ψ_(q) < 130 10 55 ≤ φ_(q) < 65  35 ≤θ_(q) ≤ 125 110 ≤ ψ_(q) < 130 11 65 ≤ φ_(q) < 75  45 ≤ θ_(q) ≤ 125 110 ≤ψ_(q) < 130 12 75 ≤ φ_(q) < 85  45 ≤ θ_(q) ≤ 135 110 ≤ ψ_(q) < 130 13 85≤ φ_(q) < 95  5 ≤ θ_(q) ≤ 25 110 ≤ ψ_(q) < 130 14 85 ≤ φ_(q) < 95  85 ≤θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 15  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 45 110 ≤ψ_(q) < 130 16  95 ≤ φ_(q) < 105 105 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 17105 ≤ φ_(q) < 115 −5 ≤ θ_(q) ≤ 45 110 ≤ ψ_(q) < 130 18 105 ≤ φ_(q) < 115135 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 19 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 45110 ≤ ψ_(q) < 130 20 115 ≤ φ_(q) < 125 145 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) <130 21 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 55 110 ≤ ψ_(q) < 130 22 125 ≤φ_(q) < 135 145 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 23 135 ≤ φ_(q) < 145 −5≤ θ_(q) ≤ 55 110 ≤ ψ_(q) < 130 24 135 ≤ φ_(q) < 145 155 ≤ θ_(q) ≤ 185110 ≤ ψ_(q) < 130 25 145 ≤ φ_(q) < 155  5 ≤ θ_(q) ≤ 75 110 ≤ ψ_(q) < 13026 155 ≤ φ_(q) < 165 25 ≤ θ_(q) ≤ 95 110 ≤ ψ_(q) < 130 27 165 ≤ φ_(q) <175  35 ≤ θ_(q) ≤ 105 110 ≤ ψ_(q) < 130 28 175 ≤ φ_(q) < 185  35 ≤ θ_(q)≤ 125 110 ≤ ψ_(q) < 130

TABLE 18 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 65 130 ≤ ψ_(q) < 150 2 −5 ≤ φ_(q) < 5  155 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 3  5 ≤ φ_(q) < 15  5 ≤ θ_(q) ≤ 65 130 ≤ψ_(q) < 150 4  5 ≤ φ_(q) < 15 145 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 5 15 ≤φ_(q) < 25 15 ≤ θ_(q) ≤ 75 130 ≤ ψ_(q) < 150 6 15 ≤ φ_(q) < 25 145 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 7 25 ≤ φ_(q) < 35 25 ≤ θ_(q) ≤ 85 130 ≤ψ_(q) < 150 8 25 ≤ φ_(q) < 35 155 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 9 35 ≤φ_(q) < 45 25 ≤ θ_(q) ≤ 95 130 ≤ ψ_(q) < 150 10 35 ≤ φ_(q) < 45 165 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 11 45 ≤ φ_(q) < 55 35 ≤ θ_(q) ≤ 95 130 ≤ψ_(q) < 150 12 55 ≤ φ_(q) < 65  25 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 13 65≤ φ_(q) < 75  5 ≤ θ_(q) ≤ 65 130 ≤ ψ_(q) < 150 14 65 ≤ φ_(q) < 75  85 ≤θ_(q) ≤ 115 130 ≤ ψ_(q) < 150 15 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 55 130 ≤ψ_(q) < 150 16 75 ≤ φ_(q) < 85 75 ≤ θ_(q) ≤ 85 130 ≤ ψ_(q) < 150 17 75 ≤φ_(q) < 85 105 ≤ θ_(q) ≤ 125 130 ≤ ψ_(q) < 150 18 85 ≤ φ_(q) < 95 −5 ≤θ_(q) ≤ 55 130 ≤ ψ_(q) < 150 19 85 ≤ φ_(q) < 95 105 ≤ θ_(q) ≤ 115 130 ≤ψ_(q) < 150 20  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 45 130 ≤ ψ_(q) < 150 21105 ≤ φ_(q) < 115 −5 ≤ θ_(q) ≤ 55 130 ≤ ψ_(q) < 150 22 115 ≤ φ_(q) < 125−5 ≤ θ_(q) ≤ 65 130 ≤ ψ_(q) < 150 23 115 ≤ φ_(q) < 125 155 ≤ θ_(q) ≤ 185130 ≤ ψ_(q) < 150 24 125 ≤ φ_(q) < 135  5 ≤ θ_(q) ≤ 65 130 ≤ ψ_(q) < 15025 125 ≤ φ_(q) < 135 145 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 26 135 ≤ φ_(q)< 145 15 ≤ θ_(q) ≤ 75 130 ≤ ψ_(q) < 150 27 135 ≤ φ_(q) < 145 145 ≤ θ_(q)≤ 185 130 ≤ ψ_(q) < 150 28 145 ≤ φ_(q) < 155 25 ≤ θ_(q) ≤ 85 130 ≤ ψ_(q)< 150 29 145 ≤ φ_(q) < 155 155 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 30 155 ≤φ_(q) < 165 25 ≤ θ_(q) ≤ 95 130 ≤ ψ_(q) < 150 31 155 ≤ φ_(q) < 165 165 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 32 165 ≤ φ_(q) < 175 35 ≤ θ_(q) ≤ 95 130 ≤ψ_(q) < 150 33 175 ≤ φ_(q) < 185  25 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150

TABLE 19 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  15 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 2  5 ≤ φ_(q) < 15 25 ≤θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 3 15 ≤ φ_(q) < 25 25 ≤ θ_(q) ≤ 85 150 ≤ψ_(q) < 170 4 15 ≤ φ_(q) < 25 165 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 5 25 ≤φ_(q) < 35 25 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 6 25 ≤ φ_(q) < 35 155 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 7 35 ≤ φ_(q) < 45 25 ≤ θ_(q) ≤ 85 150 ≤ψ_(q) < 170 8 35 ≤ φ_(q) < 45 155 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 9 45 ≤φ_(q) < 55  5 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 10 45 ≤ φ_(q) < 55 155 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 11 55 ≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 85 150 ≤ψ_(q) < 170 12 55 ≤ φ_(q) < 65 165 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 13 65≤ φ_(q) < 75 −5 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 14 75 ≤ φ_(q) < 85 −5 ≤θ_(q) ≤ 75 150 ≤ ψ_(q) < 170 15 85 ≤ φ_(q) < 95 −5 ≤ θ_(q) ≤ 65 150 ≤ψ_(q) < 170 16  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 75 150 ≤ ψ_(q) < 170 17105 ≤ φ_(q) < 115  5 ≤ θ_(q) ≤ 75 150 ≤ ψ_(q) < 170 18 115 ≤ φ_(q) < 12515 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 19 125 ≤ φ_(q) < 135 25 ≤ θ_(q) ≤ 85150 ≤ ψ_(q) < 170 20 135 ≤ φ_(q) < 145 25 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 17021 135 ≤ φ_(q) < 145 165 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 22 145 ≤ φ_(q)< 155 25 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 23 145 ≤ φ_(q) < 155 155 ≤ θ_(q)≤ 185 150 ≤ ψ_(q) < 170 24 155 ≤ φ_(q) < 165 25 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q)< 170 25 155 ≤ φ_(q) < 165 155 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 26 165 ≤φ_(q) < 175  5 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 27 165 ≤ φ_(q) < 175 155 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 28 175 ≤ φ_(q) < 185 −5 ≤ θ_(q) ≤ 85 150 ≤ψ_(q) < 170 29 175 ≤ φ_(q) < 185 165 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170

TABLE 20 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  25 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 2  5 ≤ φ_(q) < 15 25 ≤θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 3 15 ≤ φ_(q) < 25 15 ≤ θ_(q) ≤ 85 170 ≤ψ_(q) ≤ 190 4 25 ≤ φ_(q) < 35  5 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 5 35 ≤φ_(q) < 45 −5 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 6 35 ≤ φ_(q) < 45 165 ≤θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 7 45 ≤ φ_(q) < 55 −5 ≤ θ_(q) ≤ 75 170 ≤ψ_(q) ≤ 190 8 45 ≤ φ_(q) < 55 155 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 9 55 ≤φ_(q) < 65 −5 ≤ θ_(q) ≤ 75 170 ≤ ψ_(q) ≤ 190 10 55 ≤ φ_(q) < 65 155 ≤θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 11 65 ≤ φ_(q) < 75 −5 ≤ θ_(q) ≤ 85 170 ≤ψ_(q) ≤ 190 12 65 ≤ φ_(q) < 75 155 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 13 75≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 14 75 ≤ φ_(q) < 85 165 ≤θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 15 85 ≤ φ_(q) < 95  5 ≤ θ_(q) ≤ 85 170 ≤ψ_(q) ≤ 190 16  95 ≤ φ_(q) < 105 15 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 17105 ≤ φ_(q) < 115 25 ≤ θ_(q) ≤ 45 170 ≤ ψ_(q) ≤ 190 18 105 ≤ φ_(q) < 11555 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 19 115 ≤ φ_(q) < 125 25 ≤ θ_(q) ≤ 85170 ≤ ψ_(q) ≤ 190 20 125 ≤ φ_(q) < 135 25 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 19021 135 ≤ φ_(q) < 145 15 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 22 145 ≤ φ_(q) <155  5 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 23 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤85 170 ≤ ψ_(q) ≤ 190 24 155 ≤ φ_(q) < 165 165 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q)≤ 190 25 165 ≤ φ_(q) < 175 −5 ≤ θ_(q) ≤ 75 170 ≤ ψ_(q) ≤ 190 26 165 ≤φ_(q) < 175 155 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 27 175 ≤ φ_(q) < 185 −5≤ θ_(q) ≤ 75 170 ≤ ψ_(q) ≤ 190 28 175 ≤ φ_(q) < 185 155 ≤ θ_(q) ≤ 185170 ≤ ψ_(q) ≤ 190

In Tables 1 to 20, there are given the combinations of φ_(q), θ_(q), andψ_(q) in the azimuthal angles of the quartz-crystal layer 4 when the cutangle of the lithium tantalate of the piezoelectric layer 5 is about 20°Y or more and about 90° Y or less, for example. As described above, arelative bandwidth can be sufficiently widened when the cut angle of thelithium tantalate of the piezoelectric layer 5 is about 20° Y or moreand about 90° Y or less, for example.

As FIG. 1 illustrates, in the multilayer substrate 6 in the firstpreferred embodiment, the quartz-crystal layer 4 is directly disposed onthe support substrate 2. Note that the quartz-crystal layer 4 may beindirectly disposed on the support substrate 2 with another layerinterposed therebetween.

FIG. 16 is a front sectional view of the vicinity of a pair of electrodefingers in a modification of the first preferred embodiment.

A multilayer substrate 26 in the present modification includes anintermediate layer 23 disposed between the support substrate 2 and thequartz-crystal layer 4. Examples of the material for the intermediatelayer 23 include a dielectric of silicon oxide, silicon nitride, orsilicon oxynitride. Note that the intermediate layer 23 may be amultilayer body. In such a case, for example, the intermediate layer 23includes at least a first layer and a second layer. Examples of thematerial for each of the layers of the intermediate layer 23 include adielectric of silicon oxide, silicon nitride, or silicon oxynitride.

In the present modification, the higher-order mode can also besuppressed in a wide band as in the first preferred embodiment.

While preferred embodiments of the present invention have been describedabove, it is to be understood that variations and modifications will beapparent to those skilled in the art without departing from the scopeand spirit of the present invention. The scope of the present invention,therefore, is to be determined solely by the following claims.

What is claimed is:
 1. An acoustic wave device comprising: a supportsubstrate; a silicon oxide layer provided directly or indirectly on thesupport substrate and having crystallinity; a piezoelectric layer on thesilicon oxide layer having crystallinity; and an IDT electrode on thepiezoelectric layer; wherein when λ represents a wavelength defined byan electrode finger pitch of the IDT electrode, a thickness of thesilicon oxide layer having crystallinity is about 0.2λ or more and about0.4λ or less; and the piezoelectric layer has a thickness smaller thanthe thickness of the silicon oxide layer having crystallinity.
 2. Theacoustic wave device according to claim 1, wherein the silicon oxidelayer having crystallinity is a quartz-crystal layer.
 3. The acousticwave device according to claim 1, wherein the support substrate is asilicon substrate.
 4. The acoustic wave device according to claim 1,wherein the piezoelectric layer is a lithium tantalate layer; and a cutangle of lithium tantalate of the piezoelectric layer is about 20° Y ormore and about 90° Y or less.
 5. The acoustic wave device according toclaim 4, wherein the cut angle of the lithium tantalate of thepiezoelectric layer is about 20° Y or more and less than about 40° Y;the silicon oxide layer having crystallinity is a monocrystallinequartz-crystal layer; and when (φ_(q), θ_(q), ψ_(q)) represent azimuthalangles of the monocrystalline quartz-crystal layer, the angles φ_(q),θ_(q), and ψ_(q) are in any one of combinations in Tables 1 to 10: TABLE1 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤ φ_(q) <5  15 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 2 −5 ≤ φ_(q) < 5   75 ≤ θ_(q) ≤ 135−10 ≤ ψ_(q) < 10 3  5 ≤ φ_(q) < 15  5 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 4  5≤ φ_(q) < 15  65 ≤ θ_(q) ≤ 115 −10 ≤ ψ_(q) < 10 5 15 ≤ φ_(q) < 25  5 ≤θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 6 15 ≤ φ_(q) < 25  65 ≤ θ_(q) ≤ 105 −10 ≤ψ_(q) < 10 7 15 ≤ φ_(q) < 25 175 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 8 25 ≤φ_(q) < 35  −5 ≤ θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 9 25 ≤ φ_(q) < 35 155 ≤θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 10 35 ≤ φ_(q) < 45  −5 ≤ θ_(q) ≤ 105 −10 ≤ψ_(q) < 10 11 35 ≤ φ_(q) < 45 155 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 12 45 ≤φ_(q) < 55 25 ≤ θ_(q) ≤ 95 −10 ≤ ψ_(q) < 10 13 45 ≤ φ_(q) < 55 145 ≤θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 14 55 ≤ φ_(q) < 65 25 ≤ θ_(q) ≤ 95 −10 ≤ψ_(q) < 10 15 55 ≤ φ_(q) < 65 145 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 16 65 ≤φ_(q) < 75 25 ≤ θ_(q) ≤ 95 −10 ≤ ψ_(q) < 10 17 65 ≤ φ_(q) < 75 145 ≤θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 18 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 95 −10 ≤ψ_(q) < 10 19 75 ≤ φ_(q) < 85 155 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 20 85 ≤φ_(q) < 95 −5 ≤ θ_(q) ≤ 45 −10 ≤ ψ_(q) < 10 21 85 ≤ φ_(q) < 95  55 ≤θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 22 85 ≤ φ_(q) < 95 155 ≤ θ_(q) ≤ 185 −10 ≤ψ_(q) < 10 23  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 24  95≤ φ_(q) < 105  65 ≤ θ_(q) ≤ 115 −10 ≤ ψ_(q) < 10 25 105 ≤ φ_(q) < 115 15≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 26 105 ≤ φ_(q) < 115  75 ≤ θ_(q) ≤ 125 −10≤ ψ_(q) < 10 27 115 ≤ φ_(q) < 125 15 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 28115 ≤ φ_(q) < 125  75 ≤ θ_(q) ≤ 135 −10 ≤ ψ_(q) < 10 29 125 ≤ φ_(q) <135  5 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) < 10 30 125 ≤ φ_(q) < 135  65 ≤ θ_(q) ≤115 −10 ≤ ψ_(q) < 10 31 135 ≤ φ_(q) < 145  5 ≤ θ_(q) ≤ 35 −10 ≤ ψ_(q) <10 32 135 ≤ φ_(q) < 145  65 ≤ θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 33 135 ≤φ_(q) < 145 175 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 34 145 ≤ φ_(q) < 155  −5≤ θ_(q) ≤ 105 −10 ≤ ψ_(q) < 10 35 145 ≤ φ_(q) < 155 155 ≤ θ_(q) ≤ 185−10 ≤ ψ_(q) < 10 36 155 ≤ φ_(q) < 165  −5 ≤ θ_(q) ≤ 105 −10 ≤ ψ_(q) < 1037 155 ≤ φ_(q) < 165 155 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 38 165 ≤ φ_(q) <175 25 ≤ θ_(q) ≤ 95 −10 ≤ ψ_(q) < 10 39 165 ≤ φ_(q) < 175 145 ≤ θ_(q) ≤175 −10 ≤ ψ_(q) < 10 40 175 ≤ φ_(q) < 185 25 ≤ θ_(q) ≤ 95 −10 ≤ ψ_(q) <10 41 175 ≤ φ_(q) < 185 145 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10

TABLE 2 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   5 ≤ θ_(q) ≤ 35 10 ≤ ψ_(q) < 30 2 −5 ≤ φ_(q) < 5   65 ≤ θ_(q)≤ 145 10 ≤ ψ_(q) < 30 3  5 ≤ φ_(q) < 15  −5 ≤ θ_(q) ≤ 145 10 ≤ ψ_(q) <30 4 15 ≤ φ_(q) < 25  −5 ≤ θ_(q) ≤ 135 10 ≤ ψ_(q) < 30 5 25 ≤ φ_(q) < 35 25 ≤ θ_(q) ≤ 135 10 ≤ ψ_(q) < 30 6 35 ≤ φ_(q) < 45  25 ≤ θ_(q) ≤ 125 10≤ ψ_(q) < 30 7 35 ≤ φ_(q) < 45 175 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 8 45 ≤φ_(q) < 55  25 ≤ θ_(q) ≤ 105 10 ≤ ψ_(q) < 30 9 45 ≤ φ_(q) < 55 165 ≤θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 10 55 ≤ φ_(q) < 65  −5 ≤ θ_(q) ≤ 105 10 ≤ψ_(q) < 30 11 55 ≤ φ_(q) < 65 155 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 12 65 ≤φ_(q) < 75  −5 ≤ θ_(q) ≤ 105 10 ≤ ψ_(q) < 30 13 65 ≤ φ_(q) < 75 145 ≤θ_(q) ≤ 175 10 ≤ ψ_(q) < 30 14 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 45 10 ≤ψ_(q) < 30 15 75 ≤ φ_(q) < 85 75 ≤ θ_(q) ≤ 95 10 ≤ ψ_(q) < 30 16 75 ≤φ_(q) < 85 145 ≤ θ_(q) ≤ 165 10 ≤ ψ_(q) < 30 17 85 ≤ φ_(q) < 95 15 ≤θ_(q) ≤ 35 10 ≤ ψ_(q) < 30 18 85 ≤ φ_(q) < 95 75 ≤ θ_(q) ≤ 95 10 ≤ ψ_(q)< 30 19 85 ≤ φ_(q) < 95 145 ≤ θ_(q) ≤ 175 10 ≤ ψ_(q) < 30 20  95 ≤ φ_(q)< 105 15 ≤ θ_(q) ≤ 35 10 ≤ ψ_(q) < 30 21  95 ≤ φ_(q) < 105 65 ≤ θ_(q) ≤95 10 ≤ ψ_(q) < 30 22  95 ≤ φ_(q) < 105 145 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) <30 23 105 ≤ φ_(q) < 115 15 ≤ θ_(q) ≤ 35 10 ≤ ψ_(q) < 30 24 105 ≤ φ_(q) <115 65 ≤ θ_(q) ≤ 95 10 ≤ ψ_(q) < 30 25 105 ≤ φ_(q) < 115 145 ≤ θ_(q) ≤185 10 ≤ ψ_(q) < 30 26 115 ≤ φ_(q) < 125  5 ≤ θ_(q) ≤ 35 10 ≤ ψ_(q) < 3027 115 ≤ φ_(q) < 125  65 ≤ θ_(q) ≤ 145 10 ≤ ψ_(q) < 30 28 125 ≤ φ_(q) <135  −5 ≤ θ_(q) ≤ 145 10 ≤ ψ_(q) < 30 29 135 ≤ φ_(q) < 145  −5 ≤ θ_(q) ≤135 10 ≤ ψ_(q) < 30 30 145 ≤ φ_(q) < 155  25 ≤ θ_(q) ≤ 135 10 ≤ ψ_(q) <30 31 155 ≤ φ_(q) < 165  25 ≤ θ_(q) ≤ 115 10 ≤ ψ_(q) < 30 32 155 ≤ φ_(q)< 165 175 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 33 165 ≤ φ_(q) < 175  25 ≤ θ_(q)≤ 105 10 ≤ ψ_(q) < 30 34 165 ≤ φ_(q) < 175 165 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q)< 30 35 175 ≤ φ_(q) < 185  −5 ≤ θ_(q) ≤ 105 10 ≤ ψ_(q) < 30 36 175 ≤φ_(q) < 185 155 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30

TABLE 3 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 85 30 ≤ ψ_(q) < 50 2 −5 ≤ φ_(q) < 5  125 ≤ θ_(q)≤ 185 30 ≤ ψ_(q) < 50 3  5 ≤ φ_(q) < 15 25 ≤ θ_(q) ≤ 75 30 ≤ ψ_(q) < 504  5 ≤ φ_(q) < 15 125 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 5 15 ≤ φ_(q) < 25 25≤ θ_(q) ≤ 55 30 ≤ ψ_(q) < 50 6 15 ≤ φ_(q) < 25 65 ≤ θ_(q) ≤ 85 30 ≤ψ_(q) < 50 7 15 ≤ φ_(q) < 25 125 ≤ θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 8 25 ≤φ_(q) < 35 15 ≤ θ_(q) ≤ 55 30 ≤ ψ_(q) < 50 9 25 ≤ φ_(q) < 35 115 ≤ θ_(q)≤ 145 30 ≤ ψ_(q) < 50 10 35 ≤ φ_(q) < 45 −5 ≤ θ_(q) ≤ 45 30 ≤ ψ_(q) < 5011 35 ≤ φ_(q) < 45  75 ≤ θ_(q) ≤ 145 30 ≤ ψ_(q) < 50 12 45 ≤ φ_(q) < 55−5 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 13 45 ≤ φ_(q) < 55  75 ≤ θ_(q) ≤ 135 30≤ ψ_(q) < 50 14 55 ≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 15 55 ≤φ_(q) < 65  85 ≤ θ_(q) ≤ 135 30 ≤ ψ_(q) < 50 16 55 ≤ φ_(q) < 65 175 ≤θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 17 65 2 ≤ φ_(q) < 75   15≤ θ_(q) ≤ 45 30 ≤ψ_(q) < 50 18 65 2 ≤ φ_(q) < 75   75 ≤ θ_(q) ≤ 115 30 ≤ ψ_(q) < 50 19 652 ≤ φ_(q) < 75  155 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 20 75 2 ≤ φ_(q) < 85 15 ≤ θ_(q) ≤ 45 30 ≤ ψ_(q) < 50 21 75 2 ≤ φ_(q) < 85   75 ≤ θ_(q) ≤ 10530 ≤ ψ_(q) < 50 22 75 2 ≤ φ_(q) < 85  145 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 5023 85 2 ≤ φ_(q) < 95  15 ≤ θ_(q) ≤ 45 30 ≤ ψ_(q) < 50 24 85 ≤ φ_(q) < 9555 ≤ θ_(q) ≤ 95 30 ≤ ψ_(q) < 50 25 85 ≤ φ_(q) < 95 145 ≤ θ_(q) ≤ 165 30≤ ψ_(q) < 50 26  95 ≤ φ_(q) < 105  5 ≤ θ_(q) ≤ 95 30 ≤ ψ_(q) < 50 27  95≤ φ_(q) < 105 145 ≤ θ_(q) ≤ 165 30 ≤ ψ_(q) < 50 28 105 ≤ φ_(q) < 115 −5≤ θ_(q) ≤ 85 30 ≤ ψ_(q) < 50 29 105 ≤ φ_(q) < 115 135 ≤ θ_(q) ≤ 175 30 ≤ψ_(q) < 50 30 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 85 30 ≤ ψ_(q) < 50 31 115 ≤φ_(q) < 125 125 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 32 125 ≤ φ_(q) < 135 25 ≤θ_(q) ≤ 75 30 ≤ ψ_(q) < 50 33 125 ≤ φ_(q) < 135 125 ≤ θ_(q) ≤ 185 30 ≤ψ_(q) < 50 34 135 ≤ φ_(q) < 145 25 ≤ θ_(q) ≤ 55 30 ≤ ψ_(q) < 50 35 135 ≤φ_(q) < 145 65 ≤ θ_(q) ≤ 85 30 ≤ ψ_(q) < 50 36 135 ≤ φ_(q) < 145 125 ≤θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 37 145 ≤ φ_(q) < 155 15 ≤ θ_(q) ≤ 55 30 ≤ψ_(q) < 50 38 145 ≤ φ_(q) < 155 65 ≤ θ_(q) ≤ 75 30 ≤ ψ_(q) < 50 39 145 ≤φ_(q) < 155 115 ≤ θ_(q) ≤ 145 30 ≤ ψ_(q) < 50 40 155 ≤ φ_(q) < 165 −5 ≤θ_(q) ≤ 45 30 ≤ ψ_(q) < 50 41 155 ≤ φ_(q) < 165  75 ≤ θ_(q) ≤ 145 30 ≤ψ_(q) < 50 42 165 ≤ φ_(q) < 175 −5 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 43 165 ≤φ_(q) < 175  75 ≤ θ_(q) ≤ 135 30 ≤ ψ_(q) < 50 44 175 ≤ φ_(q) < 185 −5 ≤θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 45 175 ≤ φ_(q) < 185  85 ≤ θ_(q) ≤ 135 30 ≤ψ_(q) < 50 46 175 ≤ φ_(q) < 185 175 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50

TABLE 4 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  25 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 2 −5 ≤ φ_(q) < 5  125 ≤ θ_(q)≤ 165 50 ≤ ψ_(q) < 70 3  5 ≤ φ_(q) < 15 15 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 704  5 ≤ φ_(q) < 15 105 ≤ θ_(q) ≤ 165 50 ≤ ψ_(q) < 70 5 15 ≤ φ_(q) < 25 −5≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 6 15 ≤ φ_(q) < 25  75 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 7 25 ≤ φ_(q) < 35  −5 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 8 35 ≤φ_(q) < 45  −5 ≤ θ_(q) ≤ 175 50 ≤ ψ_(q) < 70 9 45 ≤ φ_(q) < 55 25 ≤θ_(q) ≤ 85 50 ≤ ψ_(q) < 70 10 45 ≤ φ_(q) < 55  95 ≤ θ_(q) ≤ 145 50 ≤ψ_(q) < 70 11 55 ≤ φ_(q) < 65 25 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 12 55 ≤φ_(q) < 65  75 ≤ θ_(q) ≤ 145 50 ≤ ψ_(q) < 70 13 65 ≤ φ_(q) < 75  15 ≤θ_(q) ≤ 135 50 ≤ ψ_(q) < 70 14 75 ≤ φ_(q) < 85  5 ≤ θ_(q) ≤ 125 50 ≤ψ_(q) < 70 15 75 ≤ φ_(q) < 85 175 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 16 85 ≤φ_(q) < 95  −5 ≤ θ_(q) ≤ 105 50 ≤ ψ_(q) < 70 17 85 ≤ φ_(q) < 95 145 ≤θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 18  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 85 50 ≤ψ_(q) < 70 19  95 ≤ φ_(q) < 105 135 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 20 105≤ φ_(q) < 115 25 ≤ θ_(q) ≤ 75 50 ≤ ψ_(q) < 70 21 105 ≤ φ_(q) < 115 125 ≤θ_(q) ≤ 165 50 ≤ ψ_(q) < 70 22 115 ≤ φ_(q) < 125 25 ≤ θ_(q) ≤ 65 50 ≤ψ_(q) < 70 23 115 ≤ φ_(q) < 125 125 ≤ θ_(q) ≤ 165 50 ≤ ψ_(q) < 70 24 125≤ φ_(q) < 135 15 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 25 125 ≤ φ_(q) < 135 105 ≤θ_(q) ≤ 165 50 ≤ ψ_(q) < 70 26 135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 65 50 ≤ψ_(q) < 70 27 135 ≤ φ_(q) < 145  75 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 28 145≤ φ_(q) < 155  −5 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 29 155 ≤ φ_(q) < 165  −5≤ θ_(q) ≤ 175 50 ≤ ψ_(q) < 70 30 165 ≤ φ_(q) < 175 25 ≤ θ_(q) ≤ 85 50 ≤ψ_(q) < 70 31 165 ≤ φ_(q) < 175  95 ≤ θ_(q) ≤ 145 50 ≤ ψ_(q) < 70 32 175≤ φ_(q) < 185  25 ≤ θ_(q) ≤ 145 50 ≤ ψ_(q) < 70

TABLE 5 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 95  70 ≤ ψ_(q) < 90 2 −5 ≤ φ_(q) < 5  105 ≤θ_(q) ≤ 185  70 ≤ ψ_(q) < 90 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 165 70 ≤ψ_(q) < 90 4 15 ≤ φ_(q) < 25 −5 ≤ θ_(q) ≤ 155 70 ≤ ψ_(q) < 90 5 25 ≤φ_(q) < 35 35 ≤ θ_(q) ≤ 165 70 ≤ ψ_(q) < 90 6 35 ≤ φ_(q) < 45 35 ≤ θ_(q)≤ 185 70 ≤ ψ_(q) < 90 7 45 ≤ φ_(q) < 55 25 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 908 55 ≤ φ_(q) < 65  5 ≤ θ_(q) ≤ 175 70 ≤ ψ_(q) < 90 9 65 ≤ φ_(q) < 75 −5≤ θ_(q) ≤ 145 70 ≤ ψ_(q) < 90 10 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 135 70 ≤ψ_(q) < 90 11 85 ≤ φ_(q) < 95 25 ≤ θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 12  95 ≤φ_(q) < 105 25 ≤ θ_(q) ≤ 155 70 ≤ ψ_(q) < 90 13  95 ≤ φ_(q) < 105 175 ≤θ_(q) ≤ 185  70 ≤ ψ_(q) < 90 14 105 ≤ φ_(q) < 115 15 ≤ θ_(q) ≤ 95  70 ≤ψ_(q) < 90 15 105 ≤ φ_(q) < 115 105 ≤ θ_(q) ≤ 185  70 ≤ ψ_(q) < 90 16115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 95  70 ≤ ψ_(q) < 90 17 115 ≤ φ_(q) < 125105 ≤ θ_(q) ≤ 185  70 ≤ ψ_(q) < 90 18 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 16570 ≤ ψ_(q) < 90 19 135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 155 70 ≤ ψ_(q) < 90 20145 ≤ φ_(q) < 155 35 ≤ θ_(q) ≤ 165 70 ≤ ψ_(q) < 90 21 155 ≤ φ_(q) < 16535 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 22 165 ≤ φ_(q) < 175 25 ≤ θ_(q) ≤ 18570 ≤ ψ_(q) < 90 23 175 ≤ φ_(q) < 185  5 ≤ θ_(q) ≤ 175 70 ≤ ψ_(q) < 90

TABLE 6 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 5  90 ≤ ψ_(q) < 110 2 −5 ≤ φ_(q) < 5  15 ≤ θ_(q)≤ 185 90 ≤ ψ_(q) < 110 3  5 ≤ φ_(q) < 15 25 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) <110 4 15 ≤ φ_(q) < 25 35 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 5 25 ≤ φ_(q) <35 45 ≤ θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 6 35 ≤ φ_(q) < 45 5 ≤ θ_(q) ≤ 15 90≤ ψ_(q) < 110 7 35 ≤ φ_(q) < 45 25 ≤ θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 8 45 ≤φ_(q) < 55 −5 ≤ θ_(q) ≤ 165 90 ≤ ψ_(q) < 110 9 55 ≤ φ_(q) < 65 −5 ≤θ_(q) ≤ 75  90 ≤ ψ_(q) < 110 10 55 ≤ φ_(q) < 65 95 ≤ θ_(q) ≤ 185 90 ≤ψ_(q) < 110 11 65 ≤ φ_(q) < 75 15 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 12 75 ≤φ_(q) < 85 25 ≤ θ_(q) ≤ 175 90 ≤ ψ_(q) < 110 13 85 ≤ φ_(q) < 95 15 ≤θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 14  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 145 90 ≤ψ_(q) < 110 15 105 ≤ φ_(q) < 115 −5 ≤ θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 16115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 5  90 ≤ ψ_(q) < 110 17 115 ≤ φ_(q) < 12515 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 18 125 ≤ φ_(q) < 135 25 ≤ θ_(q) ≤ 18590 ≤ ψ_(q) < 110 19 135 ≤ φ_(q) < 145 35 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 11020 145 ≤ φ_(q) < 155 45 ≤ θ_(q) ≤ 155 90 ≤ ψ_(q) < 110 21 155 ≤ φ_(q) <165 5 ≤ θ_(q) ≤ 15 90 ≤ ψ_(q) < 110 22 155 ≤ φ_(q) < 165 25 ≤ θ_(q) ≤155 90 ≤ ψ_(q) < 110 23 165 ≤ φ_(q) < 175 −5 ≤ θ_(q) ≤ 165 90 ≤ ψ_(q) <110 24  175 ≤ φ_(q) ≤ 185 −5 ≤ θ_(q) ≤ 75  90 ≤ ψ_(q) < 110 25  175 ≤φ_(q) ≤ 185 95 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110

TABLE 7 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  35 ≤ θ_(q) ≤ 95 110 ≤ ψ_(q) < 130 2 −5 ≤ φ_(q) < 5  105 ≤θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 3  5 ≤ φ_(q) < 15  45 ≤ θ_(q) ≤ 165 110 ≤ψ_(q) < 130 4 15 ≤ φ_(q) < 25  45 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 5 25 ≤φ_(q) < 35 −5 ≤ θ_(q) ≤ 35 110 ≤ ψ_(q) < 130 6 25 ≤ φ_(q) < 35  65 ≤θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 7 35 ≤ φ_(q) < 45 −5 ≤ θ_(q) ≤ 45 110 ≤ψ_(q) < 130 8 35 ≤ φ_(q) < 45  85 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 9 45 ≤φ_(q) < 55 15 ≤ θ_(q) ≤ 45 110 ≤ ψ_(q) < 130 10 45 ≤ φ_(q) < 55 105 ≤θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 11 55 ≤ φ_(q) < 65 15 ≤ θ_(q) ≤ 55 110 ≤ψ_(q) < 130 12 55 ≤ φ_(q) < 65 115 ≤ θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 13 65≤ φ_(q) < 75  5 ≤ θ_(q) ≤ 65 110 ≤ ψ_(q) < 130 14 65 ≤ φ_(q) < 75 125 ≤θ_(q) ≤ 165 110 ≤ ψ_(q) < 130 15 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 75 110 ≤ψ_(q) < 130 16 75 ≤ φ_(q) < 85 125 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 17 85≤ φ_(q) < 95  −5 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 18  95 ≤ φ_(q) < 105 −5≤ θ_(q) ≤ 5  110 ≤ ψ_(q) < 130 19  95 ≤ φ_(q) < 105 15 ≤ θ_(q) ≤ 85 110≤ ψ_(q) < 130 20  95 ≤ φ_(q) < 105  95 ≤ θ_(q) ≤ 175 110 ≤ ψ_(q) < 13021 105 ≤ φ_(q) < 115  25 ≤ θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 22 115 ≤ φ_(q)< 125 35 ≤ θ_(q) ≤ 95 110 ≤ ψ_(q) < 130 23 115 ≤ φ_(q) < 125 105 ≤ θ_(q)≤ 155 110 ≤ ψ_(q) < 130 24 125 ≤ φ_(q) < 135  45 ≤ θ_(q) ≤ 165 110 ≤ψ_(q) < 130 25 135 ≤ φ_(q) < 145  45 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 26145 ≤ φ_(q) < 155 −5 ≤ θ_(q) ≤ 35 110 ≤ ψ_(q) < 130 27 145 ≤ φ_(q) < 155 65 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 28 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤ 45110 ≤ ψ_(q) < 130 29 155 ≤ φ_(q) < 165  85 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) <130 30 165 ≤ φ_(q) < 175 15 ≤ θ_(q) ≤ 45 110 ≤ ψ_(q) < 130 31 165 ≤φ_(q) < 175 105 ≤ θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 32  175 ≤ φ_(q) ≤ 185 15≤ θ_(q) ≤ 55 110 ≤ ψ_(q) < 130 33  175 ≤ φ_(q) ≤ 185 115 ≤ θ_(q) ≤ 155110 ≤ ψ_(q) < 130

TABLE 8 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   45 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 2 −5 ≤ φ_(q) < 5  115 ≤θ_(q) ≤ 175 130 ≤ ψ_(q) < 150 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 25 130 ≤ψ_(q) < 150 4  5 ≤ φ_(q) < 15  65 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 5  5 ≤φ_(q) < 15 125 ≤ θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 6 15 ≤ φ_(q) < 25 −5 ≤θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 7 15 ≤ φ_(q) < 25  65 ≤ θ_(q) ≤ 105 130 ≤ψ_(q) < 150 8 15 ≤ φ_(q) < 25 135 ≤ θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 9 25 ≤φ_(q) < 35  5 ≤ θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 10 25 ≤ φ_(q) < 35  75 ≤θ_(q) ≤ 115 130 ≤ ψ_(q) < 150 11 25 ≤ φ_(q) < 35 135 ≤ θ_(q) ≤ 165 130 ≤ψ_(q) < 150 12 35 ≤ φ_(q) < 45 15 ≤ θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 13 35 ≤φ_(q) < 45  85 ≤ θ_(q) ≤ 125 130 ≤ ψ_(q) < 150 14 35 ≤ φ_(q) < 45 145 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 15 45 ≤ φ_(q) < 55  5 ≤ θ_(q) ≤ 45 130 ≤ψ_(q) < 150 16 45 ≤ φ_(q) < 55  95 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 17 55≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 45 130 ≤ ψ_(q) < 150 18 55 ≤ φ_(q) < 65  95 ≤θ_(q) ≤ 145 130 ≤ ψ_(q) < 150 19 55 ≤ φ_(q) < 65 165 ≤ θ_(q) ≤ 185 130 ≤ψ_(q) < 150 20 65 ≤ φ_(q) < 75 −5 ≤ θ_(q) ≤ 55 130 ≤ ψ_(q) < 150 21 65 ≤φ_(q) < 75 105 ≤ θ_(q) ≤ 155 130 ≤ ψ_(q) < 150 22 75 ≤ φ_(q) < 85 −5 ≤θ_(q) ≤ 5  130 ≤ ψ_(q) < 150 23 75 ≤ φ_(q) < 85 15 ≤ θ_(q) ≤ 55 130 ≤ψ_(q) < 150 24 75 ≤ φ_(q) < 85 65 ≤ θ_(q) ≤ 85 130 ≤ ψ_(q) < 150 25 75 ≤φ_(q) < 85  95 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 26 75 ≤ φ_(q) < 85 115 ≤θ_(q) ≤ 155 130 ≤ ψ_(q) < 150 27 85 ≤ φ_(q) < 95 35 ≤ θ_(q) ≤ 65 130 ≤ψ_(q) < 150 28 85 ≤ φ_(q) < 95 85 ≤ θ_(q) ≤ 95 130 ≤ ψ_(q) < 150 29 85 ≤φ_(q) < 95 115 ≤ θ_(q) ≤ 125 130 ≤ ψ_(q) < 150 30 85 ≤ φ_(q) < 95 135 ≤θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 31  95 ≤ φ_(q) < 105 35 ≤ θ_(q) ≤ 95 130 ≤ψ_(q) < 150 32  95 ≤ φ_(q) < 105 115 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 33105 ≤ φ_(q) < 115 45 ≤ θ_(q) ≤ 95 130 ≤ ψ_(q) < 150 34 105 ≤ φ_(q) < 115135 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 35 115 ≤ φ_(q) < 125  45 ≤ θ_(q) ≤105 130 ≤ ψ_(q) < 150 36 115 ≤ φ_(q) < 125 115 ≤ θ_(q) ≤ 175 130 ≤ ψ_(q)< 150 37 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 25 130 ≤ ψ_(q) < 150 38 125 ≤φ_(q) < 135  65 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 39 125 ≤ φ_(q) < 135 125≤ θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 40 135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 35 130≤ ψ_(q) < 150 41 135 ≤ φ_(q) < 145  65 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 15042 135 ≤ φ_(q) < 145 135 ≤ θ_(q) ≤ 165 130 ≤ ψ_(q) < 150 43 145 ≤ φ_(q)< 155  5 ≤ θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 44 145 ≤ φ_(q) < 155  75 ≤ θ_(q)≤ 115 130 ≤ ψ_(q) < 150 45 145 ≤ φ_(q) < 155 135 ≤ θ_(q) ≤ 165 130 ≤ψ_(q) < 150 46 155 ≤ φ_(q) < 165 15 ≤ θ_(q) ≤ 35 130 ≤ ψ_(q) < 150 47155 ≤ φ_(q) < 165  85 ≤ θ_(q) ≤ 125 130 ≤ ψ_(q) < 150 48 155 ≤ φ_(q) <165 145 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 49 165 ≤ φ_(q) < 175  5 ≤ θ_(q)≤ 45 130 ≤ ψ_(q) < 150 50 165 ≤ φ_(q) < 175  95 ≤ θ_(q) ≤ 185 130 ≤ψ_(q) < 150 51  175 ≤ φ_(q) ≤ 185 −5 ≤ θ_(q) ≤ 45 130 ≤ ψ_(q) < 150 52 175 ≤ φ_(q) ≤ 185  95 ≤ θ_(q) ≤ 145 130 ≤ ψ_(q) < 150 53  175 ≤ φ_(q) ≤185 165 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150

TABLE 9 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 35  150 ≤ ψ_(q) < 170 2 −5 ≤ φ_(q) < 5  75 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 3  5 ≤ φ_(q) < 15 5 ≤ θ_(q) ≤ 35 150 ≤ψ_(q) < 170 4  5 ≤ φ_(q) < 15 75 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 5 15 ≤φ_(q) < 25 5 ≤ θ_(q) ≤ 35 150 ≤ ψ_(q) < 170 6 15 ≤ φ_(q) < 25 75 ≤ θ_(q)≤ 105 150 ≤ ψ_(q) < 170 7 15 ≤ φ_(q) < 25 135 ≤ θ_(q) ≤ 175  150 ≤ ψ_(q)< 170 8 25 ≤ φ_(q) < 35 5 ≤ θ_(q) ≤ 35 150 ≤ ψ_(q) < 170 9 25 ≤ φ_(q) <35 75 ≤ θ_(q) ≤ 105 150 ≤ ψ_(q) < 170 10 25 ≤ φ_(q) < 35 145 ≤ θ_(q) ≤165  150 ≤ ψ_(q) < 170 11 35 ≤ φ_(q) < 45 −5 ≤ θ_(q) ≤ 35  150 ≤ ψ_(q) <170 12 35 ≤ φ_(q) < 45 85 ≤ θ_(q) ≤ 115 150 ≤ ψ_(q) < 170 13 35 ≤ φ_(q)< 45 145 ≤ θ_(q) ≤ 165  150 ≤ ψ_(q) < 170 14 45 ≤ φ_(q) < 55 −5 ≤ θ_(q)≤ 35  150 ≤ ψ_(q) < 170 15 45 ≤ φ_(q) < 55 85 ≤ θ_(q) ≤ 115 150 ≤ ψ_(q)< 170 16 45 ≤ φ_(q) < 55 145 ≤ θ_(q) ≤ 165  150 ≤ ψ_(q) < 170 17 55 ≤φ_(q) < 65 −5 ≤ θ_(q) ≤ 5  150 ≤ ψ_(q) < 170 18 55 ≤ φ_(q) < 65 65 ≤θ_(q) ≤ 115 150 ≤ ψ_(q) < 170 19 55 ≤ φ_(q) < 65 145 ≤ θ_(q) ≤ 185  150≤ ψ_(q) < 170 20 65 ≤ φ_(q) < 75 45 ≤ θ_(q) ≤ 125 150 ≤ ψ_(q) < 170 2165 ≤ φ_(q) < 75 155 ≤ θ_(q) ≤ 185  150 ≤ ψ_(q) < 170 22 75 ≤ φ_(q) < 8545 ≤ θ_(q) ≤ 145 150 ≤ ψ_(q) < 170 23 75 ≤ φ_(q) < 85 155 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 24 85 ≤ φ_(q) < 95 45 ≤ θ_(q) ≤ 155 150 ≤ ψ_(q) < 17025  95 ≤ φ_(q) < 105 65 ≤ θ_(q) ≤ 155 150 ≤ ψ_(q) < 170 26 105 ≤ φ_(q) <115 −5 ≤ θ_(q) ≤ 15  150 ≤ ψ_(q) < 170 27 105 ≤ φ_(q) < 115 75 ≤ θ_(q) ≤165 150 ≤ ψ_(q) < 170 28 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 35  150 ≤ ψ_(q)< 170 29 115 ≤ φ_(q) < 125 75 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 30 125 ≤φ_(q) < 135 5 ≤ θ_(q) ≤ 35 150 ≤ ψ_(q) < 170 31 125 ≤ φ_(q) < 135 75 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 32 135 ≤ φ_(q) < 145 5 ≤ θ_(q) ≤ 35 150 ≤ψ_(q) < 170 33 135 ≤ φ_(q) < 145 75 ≤ θ_(q) ≤ 105 150 ≤ ψ_(q) < 170 34135 ≤ φ_(q) < 145 135 ≤ θ_(q) ≤ 175  150 ≤ ψ_(q) < 170 35 145 ≤ φ_(q) <155 5 ≤ θ_(q) ≤ 35 150 ≤ ψ_(q) < 170 36 145 ≤ φ_(q) < 155 75 ≤ θ_(q) ≤105 150 ≤ ψ_(q) < 170 37 145 ≤ φ_(q) < 155 145 ≤ θ_(q) ≤ 165  150 ≤ψ_(q) < 170 38 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤ 35  150 ≤ ψ_(q) < 170 39155 ≤ φ_(q) < 165 85 ≤ θ_(q) ≤ 115 150 ≤ ψ_(q) < 170 40 155 ≤ φ_(q) <165 145 ≤ θ_(q) ≤ 165  150 ≤ ψ_(q) < 170 41 165 ≤ φ_(q) < 175 −5 ≤ θ_(q)≤ 35  150 ≤ ψ_(q) < 170 42 165 ≤ φ_(q) < 175 85 ≤ θ_(q) ≤ 115 150 ≤ψ_(q) < 170 43 165 ≤ φ_(q) < 175 145 ≤ θ_(q) ≤ 165  150 ≤ ψ_(q) < 170 44 175 ≤ φ_(q) ≤ 185 −5 ≤ θ_(q) ≤ 5  150 ≤ ψ_(q) < 170 45  175 ≤ φ_(q) ≤185 55 ≤ θ_(q) ≤ 115 150 ≤ ψ_(q) < 170 46  175 ≤ φ_(q) ≤ 185 145 ≤ θ_(q)≤ 185  150 ≤ ψ_(q) < 170

TABLE 10 CONDI- φ_(q) θ_(q) ψ_(q) TION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  5 ≤ θ_(q) ≤ 35 170 ≤ ψ_(q) ≤ 190 2 −5 ≤ φ_(q) < 5  85 ≤ θ_(q)≤ 155 170 ≤ ψ_(q) ≤ 190 3  5 ≤ φ_(q) < 15 5 ≤ θ_(q) ≤ 35 170 ≤ ψ_(q) ≤190 4  5 ≤ φ_(q) < 15 85 ≤ θ_(q) ≤ 155 170 ≤ ψ_(q) ≤ 190 5 15 ≤ φ_(q) <25 −5 ≤ θ_(q) ≤ 25  170 ≤ ψ_(q) ≤ 190 6 15 ≤ φ_(q) < 25 75 ≤ θ_(q) ≤ 185170 ≤ ψ_(q) ≤ 190 7 25 ≤ φ_(q) < 35 −5 ≤ θ_(q) ≤ 25  170 ≤ ψ_(q) ≤ 190 825 ≤ φ_(q) < 35 75 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 9 35 ≤ φ_(q) < 45 −5≤ θ_(q) ≤ 5  170 ≤ ψ_(q) ≤ 190 10 35 ≤ φ_(q) < 45 75 ≤ θ_(q) ≤ 115 170 ≤ψ_(q) ≤ 190 11 35 ≤ φ_(q) < 45 145 ≤ θ_(q) ≤ 175  170 ≤ ψ_(q) ≤ 190 1245 ≤ φ_(q) < 55 65 ≤ θ_(q) ≤ 115 170 ≤ ψ_(q) ≤ 190 13 45 ≤ φ_(q) < 55145 ≤ θ_(q) ≤ 175  170 ≤ ψ_(q) ≤ 190 14 55 ≤ φ_(q) < 65 45 ≤ θ_(q) ≤ 105170 ≤ ψ_(q) ≤ 190 15 55 ≤ φ_(q) < 65 145 ≤ θ_(q) ≤ 165  170 ≤ ψ_(q) ≤190 16 65 ≤ φ_(q) < 75 55 ≤ θ_(q) ≤ 105 170 ≤ ψ_(q) ≤ 190 17 65 ≤ φ_(q)< 75 145 ≤ θ_(q) ≤ 165  170 ≤ ψ_(q) ≤ 190 18 75 ≤ φ_(q) < 85 65 ≤ θ_(q)≤ 115 170 ≤ ψ_(q) ≤ 190 19 75 ≤ φ_(q) < 85 145 ≤ θ_(q) ≤ 185  170 ≤ψ_(q) ≤ 190 20 85 ≤ φ_(q) < 95 −5 ≤ θ_(q) ≤ 25  170 ≤ ψ_(q) ≤ 190 21 85≤ φ_(q) < 95 75 ≤ θ_(q) ≤ 125 170 ≤ ψ_(q) ≤ 190 22 85 ≤ φ_(q) < 95 135 ≤θ_(q) ≤ 185  170 ≤ ψ_(q) ≤ 190 23  105 ≤ φ_(q) ≤ 115 5 ≤ θ_(q) ≤ 35  170≤ ψ_(q) ≤
 190.


6. The acoustic wave device according to claim 4, wherein the cut angleof the lithium tantalate of the piezoelectric layer is about 40° Y ormore and about 90° Y or less; the silicon oxide layer havingcrystallinity is a monocrystalline quartz-crystal layer; and when(φ_(q), θ_(q), ψ_(q)) represent azimuthal angles of the monocrystallinequartz-crystal layer, the angles φ_(q), θ_(q), and ψ_(q) are in any oneof combinations in Tables 11 to 20: TABLE 11 φ_(q) θ_(q) ψ_(q) CONDITIONRANGE[°] RANGE[°] RANGE[°] 1 −5 ≤ φ_(q) < 5  −5 ≤ θ_(q) ≤ 25  −10 ≤ψ_(q) < 10 2 −5 ≤ φ_(q) < 5  105 ≤ θ_(q) ≤ 185  −10 ≤ ψ_(q) < 10 3  5 ≤φ_(q) < 15 −5 ≤ θ_(q) ≤ 25  −10 ≤ ψ_(q) < 10 4  5 ≤ φ_(q) < 15 1O5 ≤θ_(q) ≤ 185  −10 ≤ ψ_(q) < 10 5 15 ≤ φ_(q) < 25 −5 ≤ θ_(q) ≤ 15  −10 ≤ψ_(q) < 10 6 15 ≤ φ_(q) < 25 95 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 7 25 ≤φ_(q) < 35 95 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 8 35 ≤ φ_(q) < 45 95 ≤θ_(q) ≤ 165 −10 ≤ ψ_(q) < 10 9 45 ≤ φ_(q) < 55 95 ≤ θ_(q) ≤ 155 −10 ≤ψ_(q) < 10 10 55 ≤ φ_(q) < 65 95 ≤ θ_(q) ≤ 155 −10 ≤ ψ_(q) < 10 11 65 ≤φ_(q) < 75 95 ≤ θ_(q) ≤ 155 −10 ≤ ψ_(q) < 10 12 75 ≤ φ_(q) < 85 95 ≤θ_(q) ≤ 165 −10 ≤ ψ_(q) < 10 13 85 ≤ φ_(q) < 95 95 ≤ θ_(q) ≤ 175 −10 ≤ψ_(q) < 10 14  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 15  −10 ≤ ψ_(q) < 10 15  95≤ φ_(q) < 105 95 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 16 105 ≤ φ_(q) < 115 −5≤ θ_(q) ≤ 25  −10 ≤ ψ_(q) < 10 17 105 ≤ φ_(q) < 115 95 ≤ θ_(q) ≤ 185 −10≤ ψ_(q) < 10 18 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 25  −10 ≤ ψ_(q) < 10 19115 ≤ φ_(q) < 125 105 ≤ θ_(q) ≤ 185  −10 ≤ ψ_(q) < 10 20 125 ≤ φ_(q) <135 −5 ≤ θ_(q) ≤ 25  −10 ≤ ψ_(q) < 10 21 125 ≤ φ_(q) < 135 105 ≤ θ_(q) ≤185  −10 ≤ ψ_(q) < 10 22 135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 15  −10 ≤ ψ_(q)< 10 23 135 ≤ φ_(q) < 145 95 ≤ θ_(q) ≤ 185 −10 ≤ ψ_(q) < 10 24 145 ≤φ_(q) < 155 95 ≤ θ_(q) ≤ 175 −10 ≤ ψ_(q) < 10 25 155 ≤ φ_(q) < 165 95 ≤θ_(q) ≤ 165 −10 ≤ ψ_(q) < 10 26 165 ≤ φ_(q) < 175 95 ≤ θ_(q) ≤ 155 −10 ≤ψ_(q) < 10 27 175 ≤ φ_(q) < 185 95 ≤ θ_(q) ≤ 155 −10 ≤ ψ_(q) < 10

TABLE 12 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 15  10 ≤ ψ_(q) < 30 2 −5 ≤ φ_(q) < 5  95 ≤ θ_(q)≤ 185 10 ≤ ψ_(q) < 30 3  5 ≤ φ_(q) < 15 115 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) <30 4 15 ≤ φ_(q) < 25 105 ≤ θ_(q) ≤ 115  10 ≤ ψ_(q) < 30 5 15 ≤ φ_(q) <25 125 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 30 6 25 ≤ φ_(q) < 35 115 ≤ θ_(q) ≤185  10 ≤ ψ_(q) < 30 7 35 ≤ φ_(q) < 45 1O5 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) <30 8 45 ≤ φ_(q) < 55 95 ≤ θ_(q) ≤ 175 10 ≤ ψ_(q) < 30 9 55 ≤ φ_(q) < 6595 ≤ θ_(q) ≤ 165 10 ≤ ψ_(q) < 30 10 65 ≤ φ_(q) < 75 95 ≤ θ_(q) ≤ 155 10≤ ψ_(q) < 30 11 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 25  10 ≤ ψ_(q) < 30 12 75 ≤φ_(q) < 85 95 ≤ θ_(q) ≤ 155 10 ≤ ψ_(q) < 30 13 85 ≤ φ_(q) < 95 −5 ≤θ_(q) ≤ 25  10 ≤ ψ_(q) < 30 14 85 ≤ φ_(q) < 95 95 ≤ θ_(q) ≤ 155 10 ≤ψ_(q) < 30 15  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 25  10 ≤ ψ_(q) < 30 16  95≤ φ_(q) < 105 95 ≤ θ_(q) ≤ 155 10 ≤ ψ_(q) < 30 17 105 ≤ φ_(q) < 115 −5 ≤θ_(q) ≤ 25  10 ≤ ψ_(q) < 30 18 105 ≤ φ_(q) < 115 95 ≤ θ_(q) ≤ 175 10 ≤ψ_(q) < 30 19 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 15  10 ≤ ψ_(q) < 30 20 115≤ φ_(q) < 125 95 ≤ θ_(q) ≤ 185 10 ≤ ψ_(q) < 30 21 125 ≤ φ_(q) < 135 115≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 30 22 135 ≤ φ_(q) < 145 105 ≤ θ_(q) ≤ 115 10 ≤ ψ_(q) < 30 23 135 ≤ φ_(q) < 145 125 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 3024 145 ≤ φ_(q) < 155 115 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 30 25 155 ≤ φ_(q) <165 105 ≤ θ_(q) ≤ 185  10 ≤ ψ_(q) < 30 26 165 ≤ φ_(q) < 175 95 ≤ θ_(q) ≤175 10 ≤ ψ_(q) < 30 27 175 ≤ φ_(q) < 185 95 ≤ θ_(q) ≤ 165 10 ≤ ψ_(q) <30

TABLE 13 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   75 ≤ θ_(q) ≤ 105 30 ≤ ψ_(q) < 50 2 −5 ≤ φ_(q) < 5  115 ≤θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 3  5 ≤ φ_(q) < 15 65 ≤ θ_(q) ≤ 95 30 ≤ ψ_(q)< 50 4  5 ≤ φ_(q) < 15 115 ≤ θ_(q) ≤ 175 30 ≤ ψ_(q) < 50 5 15 ≤ φ_(q) <25 65 ≤ θ_(q) ≤ 75 30 ≤ ψ_(q) < 50 6 15 ≤ φ_(q) < 25 145 ≤ θ_(q) ≤ 18530 ≤ ψ_(q) < 50 7 25 ≤ φ_(q) < 35 55 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 8 25 ≤φ_(q) < 35 135 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 9 35 ≤ φ_(q) < 45 135 ≤θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 10 45 ≤ φ_(q) < 55 125 ≤ θ_(q) ≤ 185 30 ≤ψ_(q) < 50 11 55 ≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 25 30 ≤ ψ_(q) < 50 12 55 ≤φ_(q) < 65 115 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 13 65 ≤ φ_(q) < 75 −5 ≤θ_(q) ≤ 35 30 ≤ ψ_(q) < 50 14 65 ≤ φ_(q) < 75 115 ≤ θ_(q) ≤ 175 30 ≤ψ_(q) < 50 15 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 25 30 ≤ ψ_(q) < 50 16 75 ≤φ_(q) < 85  95 ≤ θ_(q) ≤ 165 30 ≤ ψ_(q) < 50 17 85 ≤ φ_(q) < 95 −5 ≤θ_(q) ≤ 25 30 ≤ ψ_(q) < 50 18 85 ≤ φ_(q) < 95  95 ≤ θ_(q) ≤ 155 30 ≤ψ_(q) < 50 19  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 15 30 ≤ ψ_(q) < 50 20  95 ≤φ_(q) < 105  85 ≤ θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 21 105 ≤ φ_(q) < 115  85 ≤θ_(q) ≤ 145 30 ≤ ψ_(q) < 50 22 115 ≤ φ_(q) < 125  75 ≤ θ_(q) ≤ 105 30 ≤ψ_(q) < 50 23 115 ≤ φ_(q) < 125 115 ≤ θ_(q) ≤ 155 30 ≤ ψ_(q) < 50 24 125≤ φ_(q) < 135 65 ≤ θ_(q) ≤ 95 30 ≤ ψ_(q) < 50 25 125 ≤ φ_(q) < 135 115 ≤θ_(q) ≤ 175 30 ≤ ψ_(q) < 50 26 135 ≤ φ_(q) < 145 65 ≤ θ_(q) ≤ 75 30 ≤ψ_(q) < 50 27 135 ≤ φ_(q) < 145 145 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 28 145≤ φ_(q) < 155 55 ≤ θ_(q) ≤ 65 30 ≤ ψ_(q) < 50 29 145 ≤ φ_(q) < 155 135 ≤θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 30 155 ≤ φ_(q) < 165 135 ≤ θ_(q) ≤ 185 30 ≤ψ_(q) < 50 31 165 ≤ φ_(q) < 175 125 ≤ θ_(q) ≤ 185 30 ≤ ψ_(q) < 50 32 175≤ φ_(q) < 185 −5 ≤ θ_(q) ≤ 25 30 ≤ ψ_(q) < 50 33 175 ≤ φ_(q) < 185 115 ≤θ_(q) ≤ 185 30 ≤ ψ_(q) < 50

TABLE 14 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   55 ≤ θ_(q) ≤ 135 50 ≤ ψ_(q) < 70 2  5 ≤ φ_(q) < 15  55 ≤θ_(q) ≤ 135 50 ≤ ψ_(q) < 70 3 15 ≤ φ_(q) < 25  45 ≤ θ_(q) ≤ 115 50 ≤ψ_(q) < 70 4 25 ≤ φ_(q) < 35 45 ≤ θ_(q) ≤ 85 50 ≤ ψ_(q) < 70 5 25 ≤φ_(q) < 35 165 ≤ θ_(q) ≤ 175 50 ≤ ψ_(q) < 70 6 35 ≤ φ_(q) < 45 −5 ≤θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 7 35 ≤ φ_(q) < 45 145 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 8 45 ≤ φ_(q) < 55 −5 ≤ θ_(q) ≤ 45 50 ≤ ψ_(q) < 70 9 45 ≤φ_(q) < 55 135 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 10 55 ≤ φ_(q) < 65 −5 ≤θ_(q) ≤ 35 50 ≤ ψ_(q) < 70 11 55 ≤ φ_(q) < 65 125 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 12 65 ≤ φ_(q) < 75 −5 ≤ θ_(q) ≤ 35 50 ≤ ψ_(q) < 70 13 65 ≤φ_(q) < 75 125 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 14 75 ≤ φ_(q) < 85 −5 ≤θ_(q) ≤ 25 50 ≤ ψ_(q) < 70 15 75 ≤ φ_(q) < 85 115 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 16 85 ≤ φ_(q) < 95  95 ≤ θ_(q) ≤ 175 50 ≤ ψ_(q) < 70 17  95 ≤φ_(q) < 105  75 ≤ θ_(q) ≤ 155 50 ≤ ψ_(q) < 70 18 105 ≤ φ_(q) < 115  65 ≤θ_(q) ≤ 145 50 ≤ ψ_(q) < 70 19 115 ≤ φ_(q) < 125  65 ≤ θ_(q) ≤ 135 50 ≤ψ_(q) < 70 20 125 ≤ φ_(q) < 135  55 ≤ θ_(q) ≤ 135 50 ≤ ψ_(q) < 70 21 135≤ φ_(q) < 145  45 ≤ θ_(q) ≤ 115 50 ≤ ψ_(q) < 70 22 145 ≤ φ_(q) < 155 45≤ θ_(q) ≤ 85 50 ≤ ψ_(q) < 70 23 145 ≤ φ_(q) < 155 165 ≤ θ_(q) ≤ 175 50 ≤ψ_(q) < 70 24 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤ 65 50 ≤ ψ_(q) < 70 25 155 ≤φ_(q) < 165 145 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70 26 165 ≤ φ_(q) < 175 −5 ≤θ_(q) ≤ 45 50 ≤ ψ_(q) < 70 27 165 ≤ φ_(q) < 175 135 ≤ θ_(q) ≤ 185 50 ≤ψ_(q) < 70 28 175 ≤ φ_(q) < 185 −5 ≤ θ_(q) ≤ 35 50 ≤ ψ_(q) < 70 29 175 ≤φ_(q) < 185 125 ≤ θ_(q) ≤ 185 50 ≤ ψ_(q) < 70

TABLE 15 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5   55 ≤ θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 2  5 ≤ φ_(q) < 15 25 ≤θ_(q) ≤ 35 70 ≤ ψ_(q) < 90 3  5 ≤ φ_(q) < 15  45 ≤ θ_(q) ≤ 135 70 ≤ψ_(q) < 90 4 15 ≤ φ_(q) < 25  −5 ≤ θ_(q) ≤ 115 70 ≤ ψ_(q) < 90 5 25 ≤φ_(q) < 35 −5 ≤ θ_(q) ≤ 65 70 ≤ ψ_(q) < 90 6 35 ≤ φ_(q) < 45 −5 ≤ θ_(q)≤ 55 70 ≤ ψ_(q) < 90 7 45 ≤ φ_(q) < 55 −5 ≤ θ_(q) ≤ 45 70 ≤ ψ_(q) < 90 855 ≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 35 70 ≤ ψ_(q) < 90 9 55 ≤ φ_(q) < 65 135 ≤θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 10 65 ≤ φ_(q) < 75 125 ≤ θ_(q) ≤ 185 70 ≤ψ_(q) < 90 11 75 ≤ φ_(q) < 85 115 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 12 85 ≤φ_(q) < 95  85 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 13  95 ≤ φ_(q) < 105  65 ≤θ_(q) ≤ 185 70 ≤ ψ_(q) < 90 14 105 ≤ φ_(q) < 115  55 ≤ θ_(q) ≤ 175 70 ≤ψ_(q) < 90 15 115 ≤ φ_(q) < 125  55 ≤ θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 16 125≤ φ_(q) < 135 25 ≤ θ_(q) ≤ 35 70 ≤ ψ_(q) < 90 17 125 ≤ φ_(q) < 135  45 ≤θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 18 135 ≤ φ_(q) < 145  −5 ≤ θ_(q) ≤ 115 70 ≤ψ_(q) < 90 19 135 ≤ φ_(q) < 145 125 ≤ θ_(q) ≤ 135 70 ≤ ψ_(q) < 90 20 145≤ φ_(q) < 155 −5 ≤ θ_(q) ≤ 65 70 ≤ ψ_(q) < 90 21 155 ≤ φ_(q) < 165 −5 ≤θ_(q) ≤ 55 70 ≤ ψ_(q) < 90 22 165 ≤ φ_(q) < 175 −5 ≤ θ_(q) ≤ 45 70 ≤ψ_(q) < 90 23 175 ≤ φ_(q) < 185 −5 ≤ θ_(q) ≤ 35 70 ≤ ψ_(q) < 90 24 175 ≤φ_(q) < 185 135 ≤ θ_(q) ≤ 185 70 ≤ ψ_(q) < 90

TABLE 16 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 45 90 ≤ ψ_(q) < 110 2 −5 ≤ φ_(q) < 5  135 ≤θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 45 90 ≤ψ_(q) < 110 4  5 ≤ φ_(q) < 15 165 ≤ θ_(q) ≤ 175 90 ≤ ψ_(q) < 110 5 15 ≤φ_(q) < 25 −5 ≤ θ_(q) ≤ 65 90 ≤ ψ_(q) < 110 6 25 ≤ φ_(q) < 35 −5 ≤ θ_(q)≤ 65 90 ≤ ψ_(q) < 110 7 35 ≤ φ_(q) < 45 −5 ≤ θ_(q) ≤ 75 90 ≤ ψ_(q) < 1108 45 ≤ φ_(q) < 55  15 ≤ θ_(q) ≤ 115 90 ≤ ψ_(q) < 110 9 45 ≤ φ_(q) < 55175 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 10 55 ≤ φ_(q) < 65  35 ≤ θ_(q) ≤ 12590 ≤ ψ_(q) < 110 11 65 ≤ φ_(q) < 75  55 ≤ θ_(q) ≤ 145 90 ≤ ψ_(q) < 11012 75 ≤ φ_(q) < 85  55 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 13 85 ≤ φ_(q) < 95 65 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 14  95 ≤ φ_(q) < 105  85 ≤ θ_(q) ≤105 90 ≤ ψ_(q) < 110 15  95 ≤ φ_(q) < 105 115 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) <110 16 105 ≤ φ_(q) < 115 125 ≤ θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 17 115 ≤φ_(q) < 125 −5 ≤ θ_(q) ≤ 45 90 ≤ ψ_(q) < 110 18 115 ≤ φ_(q) < 125 135 ≤θ_(q) ≤ 185 90 ≤ ψ_(q) < 110 19 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 45 90 ≤ψ_(q) < 110 20 125 ≤ φ_(q) < 135 165 ≤ θ_(q) ≤ 175 90 ≤ ψ_(q) < 110 21135 ≤ φ_(q) < 145 −5 ≤ θ_(q) ≤ 65 90 ≤ ψ_(q) < 110 22 145 ≤ φ_(q) < 155−5 ≤ θ_(q) ≤ 65 90 ≤ ψ_(q) < 110 23 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤ 75 90≤ ψ_(q) < 110 24 165 ≤ φ_(q) < 175  15 ≤ θ_(q) ≤ 115 90 ≤ ψ_(q) < 110 25175 ≤ φ_(q) < 185  35 ≤ θ_(q) ≤ 125 90 ≤ ψ_(q) < 110

TABLE 17 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 45 110 ≤ ψ_(q) < 130 2 −5 ≤ φ_(q) < 5  145 ≤θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 3  5 ≤ φ_(q) < 15 −5 ≤ θ_(q) ≤ 55 110 ≤ψ_(q) < 130 4  5 ≤ φ_(q) < 15 145 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 5 15 ≤φ_(q) < 25 −5 ≤ θ_(q) ≤ 55 110 ≤ ψ_(q) < 130 6 15 ≤ φ_(q) < 25 155 ≤θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 7 25 ≤ φ_(q) < 35  5 ≤ θ_(q) ≤ 75 110 ≤ψ_(q) < 130 8 35 ≤ φ_(q) < 45 25 ≤ θ_(q) ≤ 95 110 ≤ ψ_(q) < 130 9 45 ≤φ_(q) < 55  35 ≤ θ_(q) ≤ 105 110 ≤ ψ_(q) < 130 10 55 ≤ φ_(q) < 65  35 ≤θ_(q) ≤ 125 110 ≤ ψ_(q) < 130 11 65 ≤ φ_(q) < 75  45 ≤ θ_(q) ≤ 125 110 ≤ψ_(q) < 130 12 75 ≤ φ_(q) < 85  45 ≤ θ_(q) ≤ 135 110 ≤ ψ_(q) < 130 13 85≤ φ_(q) < 95  5 ≤ θ_(q) ≤ 25 110 ≤ ψ_(q) < 130 14 85 ≤ φ_(q) < 95  85 ≤θ_(q) ≤ 155 110 ≤ ψ_(q) < 130 15  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 45 110 ≤ψ_(q) < 130 16  95 ≤ φ_(q) < 105 105 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 17105 ≤ φ_(q) < 115 −5 ≤ θ_(q) ≤ 45 110 ≤ ψ_(q) < 130 18 105 ≤ φ_(q) < 115135 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 19 115 ≤ φ_(q) < 125 −5 ≤ θ_(q) ≤ 45110 ≤ ψ_(q) < 130 20 115 ≤ φ_(q) < 125 145 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) <130 21 125 ≤ φ_(q) < 135 −5 ≤ θ_(q) ≤ 55 110 ≤ ψ_(q) < 130 22 125 ≤φ_(q) < 135 145 ≤ θ_(q) ≤ 185 110 ≤ ψ_(q) < 130 23 135 ≤ φ_(q) < 145 −5≤ θ_(q) ≤ 55 110 ≤ ψ_(q) < 130 24 135 ≤ φ_(q) < 145 155 ≤ θ_(q) ≤ 185110 ≤ ψ_(q) < 130 25 145 ≤ φ_(q) < 155  5 ≤ θ_(q) ≤ 75 110 ≤ ψ_(q) < 13026 155 ≤ φ_(q) < 165 25 ≤ θ_(q) ≤ 95 110 ≤ ψ_(q) < 130 27 165 ≤ φ_(q) <175  35 ≤ θ_(q) ≤ 105 110 ≤ ψ_(q) < 130 28 175 ≤ φ_(q) < 185  35 ≤ θ_(q)≤ 125 110 ≤ ψ_(q) < 130

TABLE 18 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  −5 ≤ θ_(q) ≤ 65 130 ≤ ψ_(q) < 150 2 −5 ≤ φ_(q) < 5  155 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 3  5 ≤ φ_(q) < 15  5 ≤ θ_(q) ≤ 65 130 ≤ψ_(q) < 150 4  5 ≤ φ_(q) < 15 145 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 5 15 ≤φ_(q) < 25 15 ≤ θ_(q) ≤ 75 130 ≤ ψ_(q) < 150 6 15 ≤ φ_(q) < 25 145 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 7 25 ≤ φ_(q) < 35 25 ≤ θ_(q) ≤ 85 130 ≤ψ_(q) < 150 8 25 ≤ φ_(q) < 35 155 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 9 35 ≤φ_(q) < 45 25 ≤ θ_(q) ≤ 95 130 ≤ ψ_(q) < 150 10 35 ≤ φ_(q) < 45 165 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 11 45 ≤ φ_(q) < 55 35 ≤ θ_(q) ≤ 95 130 ≤ψ_(q) < 150 12 55 ≤ φ_(q) < 65  25 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150 13 65≤ φ_(q) < 75  5 ≤ θ_(q) ≤ 65 130 ≤ ψ_(q) < 150 14 65 ≤ φ_(q) < 75  85 ≤θ_(q) ≤ 115 130 ≤ ψ_(q) < 150 15 75 ≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 55 130 ≤ψ_(q) < 150 16 75 ≤ φ_(q) < 85 75 ≤ θ_(q) ≤ 85 130 ≤ ψ_(q) < 150 17 75 ≤φ_(q) < 85 105 ≤ θ_(q) ≤ 125 130 ≤ ψ_(q) < 150 18 85 ≤ φ_(q) < 95 −5 ≤θ_(q) ≤ 55 130 ≤ ψ_(q) < 150 19 85 ≤ φ_(q) < 95 105 ≤ θ_(q) ≤ 115 130 ≤ψ_(q) < 150 20  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 45 130 ≤ ψ_(q) < 150 21105 ≤ φ_(q) < 115 −5 ≤ θ_(q) ≤ 55 130 ≤ ψ_(q) < 150 22 115 ≤ φ_(q) < 125−5 ≤ θ_(q) ≤ 65 130 ≤ ψ_(q) < 150 23 115 ≤ φ_(q) < 125 155 ≤ θ_(q) ≤ 185130 ≤ ψ_(q) < 150 24 125 ≤ φ_(q) < 135  5 ≤ θ_(q) ≤ 65 130 ≤ ψ_(q) < 15025 125 ≤ φ_(q) < 135 145 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 26 135 ≤ φ_(q)< 145 15 ≤ θ_(q) ≤ 75 130 ≤ ψ_(q) < 150 27 135 ≤ φ_(q) < 145 145 ≤ θ_(q)≤ 185 130 ≤ ψ_(q) < 150 28 145 ≤ φ_(q) < 155 25 ≤ θ_(q) ≤ 85 130 ≤ ψ_(q)< 150 29 145 ≤ φ_(q) < 155 155 ≤ θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 30 155 ≤φ_(q) < 165 25 ≤ θ_(q) ≤ 95 130 ≤ ψ_(q) < 150 31 155 ≤ φ_(q) < 165 165 ≤θ_(q) ≤ 185 130 ≤ ψ_(q) < 150 32 165 ≤ φ_(q) < 175 35 ≤ θ_(q) ≤ 95 130 ≤ψ_(q) < 150 33 175 ≤ φ_(q) < 185  25 ≤ θ_(q) ≤ 105 130 ≤ ψ_(q) < 150

TABLE 19 φ_(q) θ_(q) ψ_(q) CONDITION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  15 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 2  5 ≤ φ_(q) < 15 25 ≤θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 3 15 ≤ φ_(q) < 25 25 ≤ θ_(q) ≤ 85 150 ≤ψ_(q) < 170 4 15 ≤ φ_(q) < 25 165 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 5 25 ≤φ_(q) < 35 25 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 6 25 ≤ φ_(q) < 35 155 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 7 35 ≤ φ_(q) < 45 25 ≤ θ_(q) ≤ 85 150 ≤ψ_(q) < 170 8 35 ≤ φ_(q) < 45 155 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 9 45 ≤φ_(q) < 55  5 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 10 45 ≤ φ_(q) < 55 155 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 11 55 ≤ φ_(q) < 65 −5 ≤ θ_(q) ≤ 85 150 ≤ψ_(q) < 170 12 55 ≤ φ_(q) < 65 165 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 13 65≤ φ_(q) < 75 −5 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 14 75 ≤ φ_(q) < 85 −5 ≤θ_(q) ≤ 75 150 ≤ ψ_(q) < 170 15 85 ≤ φ_(q) < 95 −5 ≤ θ_(q) ≤ 65 150 ≤ψ_(q) < 170 16  95 ≤ φ_(q) < 105 −5 ≤ θ_(q) ≤ 75 150 ≤ ψ_(q) < 170 17105 ≤ φ_(q) < 115  5 ≤ θ_(q) ≤ 75 150 ≤ ψ_(q) < 170 18 115 ≤ φ_(q) < 12515 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 19 125 ≤ φ_(q) < 135 25 ≤ θ_(q) ≤ 85150 ≤ ψ_(q) < 170 20 135 ≤ φ_(q) < 145 25 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 17021 135 ≤ φ_(q) < 145 165 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 22 145 ≤ φ_(q)< 155 25 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 23 145 ≤ φ_(q) < 155 155 ≤ θ_(q)≤ 185 150 ≤ ψ_(q) < 170 24 155 ≤ φ_(q) < 165 25 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q)< 170 25 155 ≤ φ_(q) < 165 155 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 26 165 ≤φ_(q) < 175  5 ≤ θ_(q) ≤ 85 150 ≤ ψ_(q) < 170 27 165 ≤ φ_(q) < 175 155 ≤θ_(q) ≤ 185 150 ≤ ψ_(q) < 170 28 175 ≤ φ_(q) < 185 −5 ≤ θ_(q) ≤ 85 150 ≤ψ_(q) < 170 29 175 ≤ φ_(q) < 185 165 ≤ θ_(q) ≤ 185 150 ≤ ψ_(q) < 170

TABLE 20 CONDI- φ_(q) θ_(q) ψ_(q) TION RANGE[°] RANGE[°] RANGE[°] 1 −5 ≤φ_(q) < 5  25 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 2  5 ≤ φ_(q) < 15 25 ≤θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 3 15 ≤ φ_(q) < 25 15 ≤ θ_(q) ≤ 85 170 ≤ψ_(q) ≤ 190 4 25 ≤ φ_(q) < 35  5 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 5 35 ≤φ_(q) < 45 −5 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 6 35 ≤ φ_(q) < 45 165 ≤θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 7 45 ≤ φ_(q) < 55 −5 ≤ θ_(q) ≤ 75 170 ≤ψ_(q) ≤ 190 8 45 ≤ φ_(q) < 55 155 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 9 55 ≤φ_(q) < 65 −5 ≤ θ_(q) ≤ 75 170 ≤ ψ_(q) ≤ 190 10 55 ≤ φ_(q) < 65 155 ≤θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 11 65 ≤ φ_(q) < 75 −5 ≤ θ_(q) ≤ 85 170 ≤ψ_(q) ≤ 190 12 65 ≤ φ_(q) < 75 155 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 13 75≤ φ_(q) < 85 −5 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 14 75 ≤ φ_(q) < 85 165 ≤θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 15 85 ≤ φ_(q) < 95  5 ≤ θ_(q) ≤ 85 170 ≤ψ_(q) ≤ 190 16  95 ≤ φ_(q) < 105 15 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 17105 ≤ φ_(q) < 115 25 ≤ θ_(q) ≤ 45 170 ≤ ψ_(q) ≤ 190 18 105 ≤ φ_(q) < 11555 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 19 115 ≤ φ_(q) < 125 25 ≤ θ_(q) ≤ 85170 ≤ ψ_(q) ≤ 190 20 125 ≤ φ_(q) < 135 25 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 19021 135 ≤ φ_(q) < 145 15 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 22 145 ≤ φ_(q) <155  5 ≤ θ_(q) ≤ 85 170 ≤ ψ_(q) ≤ 190 23 155 ≤ φ_(q) < 165 −5 ≤ θ_(q) ≤85 170 ≤ ψ_(q) ≤ 190 24 155 ≤ φ_(q) < 165 165 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q)≤ 190 25 165 ≤ φ_(q) < 175 −5 ≤ θ_(q) ≤ 75 170 ≤ ψ_(q) ≤ 190 26 165 ≤φ_(q) < 175 155 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤ 190 27 175 ≤ φ_(q) < 185 −5≤ θ_(q) ≤ 75 170 ≤ ψ_(q) ≤ 190 28 175 ≤ φ_(q) < 185 155 ≤ θ_(q) ≤ 185 170 ≤ ψ_(q) ≤
 190.


7. The acoustic wave device according to claim 1, further comprising anintermediate layer between the support substrate and the silicon oxidelayer having crystallinity.
 8. The acoustic wave device according toclaim 1, further comprising a protective film provided on thepiezoelectric layer to cover the IDT electrode.
 9. The acoustic wavedevice according to claim 8, wherein the protective film includessilicon oxide or silicon nitride.
 10. The acoustic wave device accordingto claim 7, wherein the intermediate layer includes silicon oxide,silicon nitride, or silicon oxynitride.
 11. The acoustic wave deviceaccording to claim 7, wherein the intermediate layer includes at least afirst layer and a second layer.